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4-26 Honors Algebra Warm-up. A square with side length x is cut from a right triangle shown at the right. What value of x will result in a figure that is 3/4 of the area of the original triangle? Show how you arrived at your answer . - PowerPoint PPT Presentation
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4-26 Honors Algebra Warm-upA square with side length x is cut from a right triangle shown at the right. What value of x will result in a figure that is 3/4 of the area of the original triangle? Show how you arrived at your answer.
There are multiple ways to get the answer, check with a partner to make sure your way is reasonable.
Answer: x = 4 units
HW: p.451 #11-31odd, 32, 34
Check odds in the back of the book.
32.Sample: 8(2n +3) cm by (n – 1) cm
34. 3in x 12in x 2in
FOIL
(3x + 4)(3x – 4)=
(3x + 4)2 =
(3x – 4)2 =
= 9x2 – 16Difference of Two Squares= 9x2 + 24x + 16Perfect Square Trinomial= 9x2 – 24x + 16Perfect Square Trinonmial
Method 6: Factoring Perfect Square Trinomials
1. Check the trinomial to see if it is of the form
a2 + 2ab + b2 or a2 - 2ab + b2
3 conditions
• The first term must be a perfect square (a2)
• The last term must be a perfect square (b)2
• The middle term must be twice the product of the square roots of the first and last terms 2(a)(b).
2. If a2 + 2ab + b2, write as (a + b)2
If a2 - 2ab + b2, write as (a - b)2
Factor Perfect Square Trinomials
A. Determine whether 25x2 – 30x + 9 is a perfect square trinomial. If so, factor it.
1. Is the first term a perfect square? Yes, 25x2 = (5x)2.
2. Is the last term a perfect square? Yes, 9 = 32.
3. Is the middle term equal to 2(5x)(3)? Yes, 30x = 2(5x)(3).
Answer: Yes, (5x – 3)2 Factor using the
pattern.
Factor Perfect Square Trinomials
B. Determine whether 49y2 + 42y + 36 is a perfect square trinomial. If so, factor it.
1. Is the first term a perfect square? Yes, 49y2 = (7y)2.
2. Is the last term a perfect square? Yes, 36 = 62.
3. Is the middle term equal to 2(7y)(6)? No, 42y ≠ 2(7y)(6).
Answer: 49y2 + 42y + 36 is not a perfect square trinomial.
Factor Completely
First check for GCF, then check for perfect square trinomial.
Since 16y2+ 8y – 15 is not a perfect square trinomial,
= 16y2 + 20y – 12y – 15 m = 20 and n = –12
= (16y2 + 20y) + (–12y – 15) Group
= 4y(4y + 5) – 3(4y + 5) Factor out the GCF
Answer: (4y + 5)(4y – 3)
use ax2 + bx + c.
Factor 16y2 + 8y – 15.
Solve Equations with Repeated Factors
Solve 4x2 + 36x + 81 = 0.
(2x + 9)2 = 0 Factor the perfect square trinomial.
2x + 9 = 0 Set the repeated factor equal to zero.
2x = –9
Solve for x.
A. Solve (b – 7)2 = 36.
Answer: {1, 13}
Use the Square Root Property to Solve Equations
Square Root Property
b = 7 ± 6 Add 7 to each side.
b = 7 + 6 or b = 7 – 6 Separate into two equations.
= 13 = 1 Simplify.
b – 7 = ±6
A. A
B. B
C. C
D. D
A. {–1, 9}
B. {–1}
C. {9}
D. {0, 9}
B. Solve the equation (x – 4)2 = 25. Check your solution.