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A. 15a2 + 8ab + 3b2
B. 10a2 – 6ab – b2
C. 5a2 + 6ab – 3b2
D. 5a2 – 6ab + 3b2
Simplify (10a2 – 6ab + b2) – (5a2 – 2b2).
A. 14w3 + 56w2 – 35w
B. 14w2 + 15w – 35
C. 9w2 + 15w – 12
D. 2w2 + 15w – 5
Simplify 7w(2w2 + 8w – 5).
A. 18y5 + 72y4 – 9y3 – 36y2
B. 6y4 + 24y3 – 3y2 – 12y
C. –18y3 – 3y2 + 12y
D. 6y3 – 2y + 4
Find the product of 3y(2y2 – 1)(y + 4).
Content Standards
A.APR.6 Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.
Mathematical Practices
6 Attend to precision.
Divide a Polynomial by a Monomial
Answer: a – 3b2 + 2a2b3
Sum of quotients
Divide.
= a – 3b2 + 2a2b3 a1 – 1 = a0 or 1 and b1 – 1 = b0 or 1
Example # 1
Division Algorithm
Use long division to find (x2 – 2x – 15) ÷ (x – 5).
Answer: The quotient is x + 3. The remainder is 0.
–2x – (–5x) = 3x3(x – 5) = 3x – 15
x(x – 5) = x2 – 5x
Example # 4
Read the Test Item
Since the second factor has an exponent of –1, this is a division problem.
Solve the Test Item
Rewrite 2 – a as –a + 2.
–a(–a + 2) = a2 – 2a–5a – (–2a) = –3a3(–a + 2) = –3a + 6Subtract. 3 – 6 = –3
Divide Polynomials
The quotient is –a + 3 and the remainder is –3.
Answer: The answer is D.
Therefore, .
Divide Polynomials