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EXAMPLE 1

EXAMPLE 1. Multiply a monomial and a polynomial. Find the product 2 x 3 ( x 3 + 3 x 2 – 2 x + 5). 2 x 3 ( x 3 + 3 x 2 – 2 x + 5). Write product. = 2 x 3 ( x 3 ) + 2 x 3 (3 x 2 ) – 2 x 3 (2 x ) + 2 x 3 (5). Distributive property. = 2 x 6 + 6 x 5 – 4 x 4 + 10 x 3.

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EXAMPLE 1

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  1. EXAMPLE 1 Multiply a monomial and a polynomial Find the product 2x3(x3 + 3x2 – 2x + 5). 2x3(x3 + 3x2 – 2x + 5) Write product. = 2x3(x3) + 2x3(3x2) – 2x3(2x) + 2x3(5) Distributive property = 2x6 + 6x5 – 4x4 + 10x3 Product of powers property

  2. EXAMPLE 2 Multiply polynomials using a table Find the product(x – 4)(3x + 2). SOLUTION STEP 1 Write subtraction as addition in each polynomial. (x – 4)(3x + 2) = [x + (– 4)](3x + 2)

  3. ANSWER The product is 3x2 + 2x – 12x – 8, or 3x2 – 10x – 8. 2 2 3x 3x x x 3x2 2x 3x2 – 12x – 8 – 4 – 4 EXAMPLE 2 Multiply polynomials using a table STEP2 Make a table of products.

  4. ANSWER ANSWER 7x3 + 4x 2a2 + 7a + 3 4n2 + 19n – 5 ANSWER for Examples 1 and 2 GUIDED PRACTICE Find the product. 1. x(7x2 +4) 2. (a +3)(2a +1) 3. (4n – 1)(n + 5)

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