The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Name Date

WORKSHEET 5.7: MULTIPLYING A POLYNOMIAL

BY A MONOMIAL

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Follow the steps below to multiply a polynomial by a monomial:

1. Multiply each term of the polynomial by the monomial. (Use the distributive property,
   a(b+c)=ab+ac, and multiply the monomials using the property of exponents for
   multiplication,xm+xn=xm+n.)


2. Find the sum.

EXAMPLE

− 8 x^4 (2x^2 − 7 x+5)=(− 8 x^4 )(2x^2 )+(− 8 x^4 )(− 7 x)+(− 8 x^4 )(5)=− 16 x^6 + 56 x^5 − 40 x^4

DIRECTIONS: Find the product.

1. 5(x+2) 2. 3(x−4) 3. 4 x(x+5)


2. 2 x^2 (x^3 −7) 5. − 3 a(4a^2 +1) 6. 5 a^2 (6a^4 −7)


3. 8 x^2 y(3x^2 + 4 xy) 8. 7 x^2 (x^3 + 5 x−2) 9. 6 a^2 b^2 (a+ 4 a^3 b+ 8 b^2 )

CHALLENGE:Khalil said that 3x(x+2)+ 4 x(x−5)= 3 x^2 + 6 x+ 4 x^2 − 20 x.Is

he correct? Explain.

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2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.