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Math Superpowers for Every Student Award-winning Photomath app makes math easy to
understand and master photomath.net
Get ready for Algebra II
Practice important Algebra II concepts with these advanced problems. In some cases, you will need to apply multiple math concepts to determine the best or most
appropriate solution format. Full solutions are at the end for your reference.
Good luck!
Question 1. What is the slope of the graph of the equation?
Question 4. Which factorizations are incorrect?
Question 3. Simplify where is the imaginary unit
Question 2. Find algebraically the zeros for by factoring
1
Get ready for Algebra II
Practice important Algebra II concepts with these advanced problems. Insome cases, you will need to apply multiple math concepts to determine thebest or most appropriate solution format. Full solutions are at the end for
your reference. Good luck!
Question 1. What is the slope of the graph of the
equation −2x+ y =3
2?
Question 2. Find algebraically the zeros forp(x) = x3 + 2x2 − 4x− 8 by factoring
Question 3. Simplify xi(i − 7i)2 where i is theimaginary unit
Question 4. Which factorizations are incorrect?
A. 4x2 − 49 = (2x+ 7)(2x− 7)
B. m3 − 8y3 = (m− 2y)(m2 + 2my + 4y2)
C. a3 + 3a2 − 4a+ 12 = (a− 2)2(a+ 3)
D. k3 + 5k2 + 6k + k2 + 5k + 6 = (k + 1)(k + 2)(k + 3)
1
Get ready for Algebra II
Practice important Algebra II concepts with these advanced problems. Insome cases, you will need to apply multiple math concepts to determine thebest or most appropriate solution format. Full solutions are at the end for
your reference. Good luck!
Question 1. What is the slope of the graph of the
equation −2x+ y =3
2?
Question 2. Find algebraically the zeros for
p(x) = x3 + 2x2 − 4x− 8 by factoring
Question 3. Simplify xi(i − 7i)2 where i is theimaginary unit
Question 4. Which factorizations are incorrect?
A. 4x2 − 49 = (2x+ 7)(2x− 7)
B. m3 − 8y3 = (m− 2y)(m2 + 2my + 4y2)
C. a3 + 3a2 − 4a+ 12 = (a− 2)2(a+ 3)
D. k3 + 5k2 + 6k + k2 + 5k + 6 = (k + 1)(k + 2)(k + 3)
1
Get ready for Algebra II
Practice important Algebra II concepts with these advanced problems. Insome cases, you will need to apply multiple math concepts to determine thebest or most appropriate solution format. Full solutions are at the end for
your reference. Good luck!
Question 1. What is the slope of the graph of the
equation −2x+ y =3
2?
Question 2. Find algebraically the zeros forp(x) = x3 + 2x2 − 4x− 8 by factoring
Question 3. Simplify xi(i − 7i)2 where i is theimaginary unit
Question 4. Which factorizations are incorrect?
A. 4x2 − 49 = (2x+ 7)(2x− 7)
B. m3 − 8y3 = (m− 2y)(m2 + 2my + 4y2)
C. a3 + 3a2 − 4a+ 12 = (a− 2)2(a+ 3)
D. k3 + 5k2 + 6k + k2 + 5k + 6 = (k + 1)(k + 2)(k + 3)
1
Get ready for Algebra II
Practice important Algebra II concepts with these advanced problems. Insome cases, you will need to apply multiple math concepts to determine thebest or most appropriate solution format. Full solutions are at the end for
your reference. Good luck!
Question 1. What is the slope of the graph of the
equation −2x+ y =3
2?
Question 2. Find algebraically the zeros forp(x) = x3 + 2x2 − 4x− 8 by factoring
Question 3. Simplify xi(i − 7i)2 where i is theimaginary unit
Question 4. Which factorizations are incorrect?
A. 4x2 − 49 = (2x+ 7)(2x− 7)
B. m3 − 8y3 = (m− 2y)(m2 + 2my + 4y2)
C. a3 + 3a2 − 4a+ 12 = (a− 2)2(a+ 3)
D. k3 + 5k2 + 6k + k2 + 5k + 6 = (k + 1)(k + 2)(k + 3)
1
Get ready for Algebra II
Practice important Algebra II concepts with these advanced problems. Insome cases, you will need to apply multiple math concepts to determine thebest or most appropriate solution format. Full solutions are at the end for
your reference. Good luck!
Question 1. What is the slope of the graph of the
equation −2x+ y =3
2?
Question 2. Find algebraically the zeros forp(x) = x3 + 2x2 − 4x− 8 by factoring
Question 3. Simplify xi(i − 7i)2 where i is theimaginary unit
Question 4. Which factorizations are incorrect?
A. 4x2 − 49 = (2x+ 7)(2x− 7)
B. m3 − 8y3 = (m− 2y)(m2 + 2my + 4y2)
C. a3 + 3a2 − 4a+ 12 = (a− 2)2(a+ 3)
D. k3 + 5k2 + 6k + k2 + 5k + 6 = (k + 1)(k + 2)(k + 3)
1
2
Question 5. What is the solution to
Question 6. Over the set of integers, factor this expression completely:
Question 7. Graph
?Question 5. What is the solution to8(2x+3)− 48 = 0?
A. 0 B. ln 2− 4 C. −2 log2 3 D. 2 + log2 3
Question 6. Over the set of integers, factor thisexpression completely:
4x3 − x2 + 16x− 4
Question 7. Graph y = 2 + log2(x+ 3)− 5
Question 8. Label the axes and graph the equa-tion y = 400(.85)2x − 6
Question 9. The graph of the equation y = 3x2
has its vertex at the coordinate point (0, 0). Whatcoordinate point describes the vertex of the graphof the equation y = 3x2 − 3 ?
A. (0, 3) B. (−3, 0) C. (3, 0) D. (0,−3)
2
Question 5. What is the solution to8(2x+3)− 48 = 0?
A. 0 B. ln 2− 4 C. −2 log2 3 D. 2 + log2 3
Question 6. Over the set of integers, factor thisexpression completely:
4x3 − x2 + 16x− 4
Question 7. Graph y = 2 + log2(x+ 3)− 5
Question 8. Label the axes and graph the equa-tion y = 400(.85)2x − 6
Question 9. The graph of the equation y = 3x2
has its vertex at the coordinate point (0, 0). Whatcoordinate point describes the vertex of the graphof the equation y = 3x2 − 3 ?
A. (0, 3) B. (−3, 0) C. (3, 0) D. (0,−3)
2
Question 5. What is the solution to8(2x+3)− 48 = 0?
A. 0 B. ln 2− 4 C. −2 log2 3 D. 2 + log2 3
Question 6. Over the set of integers, factor thisexpression completely:
4x3 − x2 + 16x− 4
Question 7. Graph y = 2 + log2(x+ 3)− 5
Question 8. Label the axes and graph the equa-tion y = 400(.85)2x − 6
Question 9. The graph of the equation y = 3x2
has its vertex at the coordinate point (0, 0). Whatcoordinate point describes the vertex of the graphof the equation y = 3x2 − 3 ?
A. (0, 3) B. (−3, 0) C. (3, 0) D. (0,−3)
2
Question 5. What is the solution to8(2x+3)− 48 = 0?
A. 0 B. ln 2− 4 C. −2 log2 3 D. 2 + log2 3
Question 6. Over the set of integers, factor thisexpression completely:
4x3 − x2 + 16x− 4
Question 7. Graph y = 2 + log2(x+ 3)− 5
Question 8. Label the axes and graph the equa-tion y = 400(.85)2x − 6
Question 9. The graph of the equation y = 3x2
has its vertex at the coordinate point (0, 0). Whatcoordinate point describes the vertex of the graphof the equation y = 3x2 − 3 ?
A. (0, 3) B. (−3, 0) C. (3, 0) D. (0,−3)
2
3
Question 9. The graph of the equation has its vertex at the coordinate point . What coordinate point describes the vertex of the graph of the equation ?
Question 8. Label the axes and graph the equation
Question 5. What is the solution to8(2x+3)− 48 = 0?
A. 0 B. ln 2− 4 C. −2 log2 3 D. 2 + log2 3
Question 6. Over the set of integers, factor thisexpression completely:
4x3 − x2 + 16x− 4
Question 7. Graph y = 2 + log2(x+ 3)− 5
Question 8. Label the axes and graph the equa-tion y = 400(.85)2x − 6
Question 9. The graph of the equation y = 3x2
has its vertex at the coordinate point (0, 0). Whatcoordinate point describes the vertex of the graphof the equation y = 3x2 − 3 ?
A. (0, 3) B. (−3, 0) C. (3, 0) D. (0,−3)
2
Question 5. What is the solution to8(2x+3)− 48 = 0?
A. 0 B. ln 2− 4 C. −2 log2 3 D. 2 + log2 3
Question 6. Over the set of integers, factor thisexpression completely:
4x3 − x2 + 16x− 4
Question 7. Graph y = 2 + log2(x+ 3)− 5
Question 8. Label the axes and graph the equa-tion y = 400(.85)2x − 6
Question 9. The graph of the equation y = 3x2
has its vertex at the coordinate point (0, 0). Whatcoordinate point describes the vertex of the graphof the equation y = 3x2 − 3 ?
A. (0, 3) B. (−3, 0) C. (3, 0) D. (0,−3)
2
Question 5. What is the solution to8(2x+3)− 48 = 0?
A. 0 B. ln 2− 4 C. −2 log2 3 D. 2 + log2 3
Question 6. Over the set of integers, factor thisexpression completely:
4x3 − x2 + 16x− 4
Question 7. Graph y = 2 + log2(x+ 3)− 5
Question 8. Label the axes and graph the equa-tion y = 400(.85)2x − 6
Question 9. The graph of the equation y = 3x2
has its vertex at the coordinate point (0, 0). Whatcoordinate point describes the vertex of the graphof the equation y = 3x2 − 3 ?
A. (0, 3) B. (−3, 0) C. (3, 0) D. (0,−3)
2
Question 5. What is the solution to8(2x+3)− 48 = 0?
A. 0 B. ln 2− 4 C. −2 log2 3 D. 2 + log2 3
Question 6. Over the set of integers, factor thisexpression completely:
4x3 − x2 + 16x− 4
Question 7. Graph y = 2 + log2(x+ 3)− 5
Question 8. Label the axes and graph the equa-tion y = 400(.85)2x − 6
Question 9. The graph of the equation y = 3x2
has its vertex at the coordinate point (0, 0). Whatcoordinate point describes the vertex of the graphof the equation y = 3x2 − 3 ?
A. (0, 3) B. (−3, 0) C. (3, 0) D. (0,−3)
2
Question 5. What is the solution to8(2x+3)− 48 = 0?
A. 0 B. ln 2− 4 C. −2 log2 3 D. 2 + log2 3
Question 6. Over the set of integers, factor thisexpression completely:
4x3 − x2 + 16x− 4
Question 7. Graph y = 2 + log2(x+ 3)− 5
Question 8. Label the axes and graph the equa-tion y = 400(.85)2x − 6
Question 9. The graph of the equation y = 3x2
has its vertex at the coordinate point (0, 0). Whatcoordinate point describes the vertex of the graphof the equation y = 3x2 − 3 ?
A. (0, 3) B. (−3, 0) C. (3, 0) D. (0,−3)
2
4
Question 10. A function of is graphed below:
Which equation best describes the graph?Question 10. A function of x is graphed below:
Which equation best describes the graph?
A. y = x2 + 5
B. y = (x+ 2)2 + 1
C. y = (x− 2)2 + 1
D. y = (x+ 2)(x− 1)
3
Question 10. A function of x is graphed below:
Which equation best describes the graph?
A. y = x2 + 5
B. y = (x+ 2)2 + 1
C. y = (x− 2)2 + 1
D. y = (x+ 2)(x− 1)
3
5
SOLUTIONS
Question 1: 2
Solving with Photomath
Option 1:
• Scan the equation in Photomath to graph it
• Use the root and vertical intercept as two random points A(x1, y1)and B(x2, y2)
• Plug in A and B into the formula for slope =y2 − y1x2 − x1
Option 2:
• Scan the equation in Photomath
• Click on the Show other methods button and select the methodto Solve the equation for y
• The equation will be shown in slope-intercept form so read outthe coefficient of the x term which represents the slope of theequation
4
SOLUTIONS
Question 1: 2
Solving with Photomath
Option 1:
• Scan the equation in Photomath to graph it
• Use the root and vertical intercept as two random points A(x1, y1)and B(x2, y2)
• Plug in A and B into the formula for slope =y2 − y1x2 − x1
Option 2:
• Scan the equation in Photomath
• Click on the Show other methods button and select the methodto Solve the equation for y
• The equation will be shown in slope-intercept form so read outthe coefficient of the x term which represents the slope of theequation
4
SOLUTIONS
Question 1: 2
Solving with Photomath
Option 1:
• Scan the equation in Photomath to graph it
• Use the root and vertical intercept as two random points A(x1, y1)and B(x2, y2)
• Plug in A and B into the formula for slope =y2 − y1x2 − x1
Option 2:
• Scan the equation in Photomath
• Click on the Show other methods button and select the methodto Solve the equation for y
• The equation will be shown in slope-intercept form so read outthe coefficient of the x term which represents the slope of theequation
4
SOLUTIONS
Question 1: 2
Solving with Photomath
Option 1:
• Scan the equation in Photomath to graph it
• Use the root and vertical intercept as two random points A(x1, y1)and B(x2, y2)
• Plug in A and B into the formula for slope =y2 − y1x2 − x1
Option 2:
• Scan the equation in Photomath
• Click on the Show other methods button and select the methodto Solve the equation for y
• The equation will be shown in slope-intercept form so read outthe coefficient of the x term which represents the slope of theequation
4
SOLUTIONS
Question 1: 2
Solving with Photomath
Option 1:
• Scan the equation in Photomath to graph it
• Use the root and vertical intercept as two random points A(x1, y1)and B(x2, y2)
• Plug in A and B into the formula for slope =y2 − y1x2 − x1
Option 2:
• Scan the equation in Photomath
• Click on the Show other methods button and select the methodto Solve the equation for y
• The equation will be shown in slope-intercept form so read outthe coefficient of the x term which represents the slope of theequation
4
Question 1: 2
Solutions
Solving with Photomath
Option 1:
• Scan the equation in Photomath to graph it
• Use the root and vertical intercept as two random points
• Plug in and into the formula for
and
6
Option 2:
• Scan the equation in Photomath
• Click on the Show other methods button and select the method to Solve the equation for y
• The equation will be shown in slope-intercept form so read out the coefficient of the term which represents the slope of the equationQuestion 10. A function of x is graphed below:
Which equation best describes the graph?
A. y = x2 + 5
B. y = (x+ 2)2 + 1
C. y = (x− 2)2 + 1
D. y = (x+ 2)(x− 1)
3
7
Question 2:−2, 2
• Scan the right side of the polynomial to factorize the expressioninto into (x+ 2)2(x− 2)
• When a function is written in the factored form, like (xp)(xq), pand q are zeros of the function. Therefore, are −2 and 2 zerosof the polynomial p(x) = (x+ 2)2(x− 2)
• Also, the first zero −2 has a multiplicity of 2 because the factoris squared
• The key here is to understand for the factored form, the zeros are−2 and 2. The first zero has a multiplicity of 2 because thefactor is squared
Question 3: −36xi
Question 4: C
Solving with Photomath
• Scan the left side of each equation and then compare the factor-ization on the right
• When you scan the left side of equation C it results in a graph.Review the final solution and compare it to the left side of theoriginal equation. You’ll see the expressions are not the sameso factorization C is incorrect
Question 5: C
Question 6: (4x− 1)(x2 + 4)
Question 7:
• Scan problem to check your answer with Photomath
Question 8:
• Scan problem to check your answer with Photomath
5
Question 2:−2, 2
• Scan the right side of the polynomial to factorize the expressioninto into (x+ 2)2(x− 2)
• When a function is written in the factored form, like (xp)(xq), pand q are zeros of the function. Therefore, are −2 and 2 zerosof the polynomial p(x) = (x+ 2)2(x− 2)
• Also, the first zero −2 has a multiplicity of 2 because the factoris squared
• The key here is to understand for the factored form, the zeros are−2 and 2. The first zero has a multiplicity of 2 because thefactor is squared
Question 3: −36xi
Question 4: C
Solving with Photomath
• Scan the left side of each equation and then compare the factor-ization on the right
• When you scan the left side of equation C it results in a graph.Review the final solution and compare it to the left side of theoriginal equation. You’ll see the expressions are not the sameso factorization C is incorrect
Question 5: C
Question 6: (4x− 1)(x2 + 4)
Question 7:
• Scan problem to check your answer with Photomath
Question 8:
• Scan problem to check your answer with Photomath
5
Question 2: -2, 2
Question 3:
Solving with Photomath
• Scan the right side of the polynomial to factorize the expression into
• Therefore, -2 and 2 are the zeros of the polynomial
of 2 because the factor is squared. Note that the first zero -2 has a multiplicity
• When a function is written in the factored form, like ,
• The most simplied expression is
p and q are zeros of the function
Question 2:−2, 2
• Scan the right side of the polynomial to factorize the expressioninto (x+ 2)2(x− 2)
• When a function is written in the factored form, like (x−p)(x−q),p and q are zeros of the function
• Therefore, are −2 and 2 zeros of the polynomial p(x) = (x +2)2(x − 2) Note that the first zero −2 has a multiplicity of 2because the factor is squared
• The most simplified expression is (x+ 2)(x+ 2)(x− 2)
Question 3: −36xi
Question 4: C
Solving with Photomath
• Scan the left side of each equation and then compare the factor-ization on the right
• When you scan the left side of equation C it results in a graph.Review the final solution and compare it to the left side of theoriginal equation. You’ll see the expressions are not the sameso factorization C is incorrect
Question 5: C
Question 6: (4x− 1)(x2 + 4)
Question 7:
• Scan problem to check your answer with Photomath
Question 8:
• Scan problem to check your answer with Photomath
5
Question 2:−2, 2
• Scan the right side of the polynomial to factorize the expressioninto (x+ 2)2(x− 2)
• When a function is written in the factored form, like (x−p)(x−q),p and q are zeros of the function
• Therefore, are −2 and 2 zeros of the polynomial p(x) = (x +2)2(x − 2) Note that the first zero −2 has a multiplicity of 2because the factor is squared
• The most simplified expression is (x+ 2)(x+ 2)(x− 2)
Question 3: −36xi
Question 4: C
Solving with Photomath
• Scan the left side of each equation and then compare the factor-ization on the right
• When you scan the left side of equation C it results in a graph.Review the final solution and compare it to the left side of theoriginal equation. You’ll see the expressions are not the sameso factorization C is incorrect
Question 5: C
Question 6: (4x− 1)(x2 + 4)
Question 7:
• Scan problem to check your answer with Photomath
Question 8:
• Scan problem to check your answer with Photomath
5
Question 2:−2, 2
• Scan the right side of the polynomial to factorize the expressioninto (x+ 2)2(x− 2)
• When a function is written in the factored form, like (x−p)(x−q),p and q are zeros of the function
• Therefore, are −2 and 2 zeros of the polynomial p(x) = (x +2)2(x − 2) Note that the first zero −2 has a multiplicity of 2because the factor is squared
• The most simplified expression is (x+ 2)(x+ 2)(x− 2)
Question 3: −36xi
Question 4: C
Solving with Photomath
• Scan the left side of each equation and then compare the factor-ization on the right
• When you scan the left side of equation C it results in a graph.Review the final solution and compare it to the left side of theoriginal equation. You’ll see the expressions are not the sameso factorization C is incorrect
Question 5: C
Question 6: (4x− 1)(x2 + 4)
Question 7:
• Scan problem to check your answer with Photomath
Question 8:
• Scan problem to check your answer with Photomath
5
Question 2:−2, 2
• Scan the right side of the polynomial to factorize the expressioninto (x+ 2)2(x− 2)
• When a function is written in the factored form, like (x−p)(x−q),p and q are zeros of the function
• Therefore, are −2 and 2 zeros of the polynomial p(x) = (x +2)2(x − 2) Note that the first zero −2 has a multiplicity of 2because the factor is squared
• The most simplified expression is (x+ 2)(x+ 2)(x− 2)
Question 3: −36xi
Question 4: C
Solving with Photomath
• Scan the left side of each equation and then compare the factor-ization on the right
• When you scan the left side of equation C it results in a graph.Review the final solution and compare it to the left side of theoriginal equation. You’ll see the expressions are not the sameso factorization C is incorrect
Question 5: C
Question 6: (4x− 1)(x2 + 4)
Question 7:
• Scan problem to check your answer with Photomath
Question 8:
• Scan problem to check your answer with Photomath
5
Question 6:
Question 2:−2, 2
• Scan the right side of the polynomial to factorize the expressioninto into (x+ 2)2(x− 2)
• When a function is written in the factored form, like (xp)(xq), pand q are zeros of the function. Therefore, are −2 and 2 zerosof the polynomial p(x) = (x+ 2)2(x− 2)
• Also, the first zero −2 has a multiplicity of 2 because the factoris squared
• The key here is to understand for the factored form, the zeros are−2 and 2. The first zero has a multiplicity of 2 because thefactor is squared
Question 3: −36xi
Question 4: C
Solving with Photomath
• Scan the left side of each equation and then compare the factor-ization on the right
• When you scan the left side of equation C it results in a graph.Review the final solution and compare it to the left side of theoriginal equation. You’ll see the expressions are not the sameso factorization C is incorrect
Question 5: C
Question 6: (4x− 1)(x2 + 4)
Question 7:
• Scan problem to check your answer with Photomath
Question 8:
• Scan problem to check your answer with Photomath
5
Question 4: C
Question 5: C
Solving with Photomath
• Scan the left side of each equation and then compare the factorization on the right
• For equation C, when you scan the left side, it results in a graph. Review the final solution and compare it to the left side of the original equation. You’ll see the expressions are not the same, so factorization C is incorrect
8
Question 7:
Question 9: D
Question 8:
Question 10: B
• Scan problem to check your answer with Photomath
• Scan problem to check your answer with Photomath
9
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