Prentice Hall Algebra 1

Chapter 8 Polynomials and Factoring > 8-2 Multiplying and Factoring

8-2 Multiplying and Factoring

Objectives

To multiply a monomial by a polynomial

To factor a monomial from a polynomial

Solve it: Anya asks, “Remember the distributive property? It can help you here.”
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Essential Understanding You can use the Distributive Property to multiply a monomial by a polynomial.

For example, consider the product 2 x open 3 x plus 1 close .

2 x ( 3 x + 1 ) = 2 x ( 3 x ) + 2 x ( 1 ) = 6 x 2 + 2 x table with 2 rows and 2 columns , row1 column 1 , 2 x open 3 x plus 1 close , column 2 equals 2 x open 3 x close plus 2 x open 1 close , row2 column 1 , , column 2 equals , 6 x squared , plus 2 x , end table

You can show why the multiplication makes sense using the area model below.

A large rectangle is divided into 8 rectangles in 2 rows of 4.
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Problem 1 Multiplying a Monomial and a Trinomial

Multiple Choice What is a simpler form of − x 3 ( 9 x 4 − 2 x 3 + 7 ) ? negative , bold italic x cubed , open , 9 bold italic x to the fourth , minus , 2 bold italic x cubed , plus 7 close question mark

− 9 x 12 + 2 x 9 − 7 x 3 negative , 9 x to the twelfth , plus , 2 x to the ninth , minus , 7 x cubed
9 x 7 − 2 x 6 + 7 x 3 9 x to the seventh , minus , 2 x to the sixth , plus , 7 x cubed
− 9 x 7 + 2 x 3 + 7 negative , 9 x to the seventh , plus , 2 x cubed , plus 7
− 9 x 7 + 2 x 6 − 7 x 3 negative , 9 x to the seventh , plus , 2 x to the sixth , minus , 7 x cubed

Plan

What should I keep in mind when multiplying?

Remember to distribute negative , x cubed to all of the terms. Also remember to add the exponents instead of multiplying them.

− x 3 ( 9 x 4 − 2 x 3 + 7 ) = − x 3 ( 9 x 4 ) − x 3 ( − 2 x 3 ) − x 3 ( 7 ) Use the Distributive Property. = − 9 x 3 + 4 + 2 x 3 + 3 − 7 x 3 Multiply coefficients and add exponents. = − 9 x 7 + 2 x 6 − 7 x 3 Simplify. table with 3 rows and 3 columns , row1 column 1 , negative , x cubed , open , 9 x to the fourth , minus , 2 x cubed , plus 7 close , column 2 equals negative , x cubed , open , 9 x to the fourth , close minus , x cubed , open negative , 2 x cubed , close minus , x cubed , open 7 close , column 3 cap usethecap distributivecap property. , row2 column 1 , , column 2 equals negative 9 , x cubed . super plus 4 end super , plus 2 , x cubed . super plus 3 end super , minus 7 , x cubed , column 3 cap multiplycoefficientsandaddexponents. , row3 column 1 , , column 2 equals negative , 9 x to the seventh , plus , 2 x to the sixth , minus , 7 x cubed , column 3 cap simplify. , end table

The correct answer is D.

✓ Got It?

What is a simpler form of 5 n ( 3 n 3 − n 2 + 8 ) ? 5 n open , 3 n cubed , minus , n squared , plus 8 close question mark

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8-2 Multiplying and Factoring

Problem 1 Multiplying a Monomial and a Trinomial

Plan

✓ Got It?

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