# Multiplying a polynomial by a monomial 8-6 objective: Students will find the product of a polynomial and a monomial. To solve equations involving polynomials.

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Multiplying a polynomial by a monomial 8-6 objective: Students will find the product of a polynomial and a monomial. To solve equations involving polynomials. S. Calahan March 2008

The Distributive Property Method 1: Horizontal -2x 2 (3x 2 – 7x + 10) -2x 2 (3x 2 ) – 2x 2 (-7x) – 2x 2 (10) - 6x 4 + 14x 3 – 20x 2

Method 2: Vertical 3x 2 – 7x + 10 x - 2x 2 x - 2x 2 -6x 4 + 14x 3 – 20x 2 -6x 4 + 14x 3 – 20x 2

Simplify Expressions 4 (3d 2 + 5d) –d (d 2 -7d + 12) 12d 2 + 20d –d 3 + 7d 2 – 12d group like terms - d 3 + (12d 2 + 7d 2 ) + (20d – 12d) add like terms -d 3 + 19d 2 + 8d

Polynomial equations d(d-1) + 4d = d(d-8) Distribute d 2 – d + 4d = d 2 – 8d Combine like terms d 2 + 3d = d 2 – 8d

Now solve for d d 2 + 3d = d 2 – 8d - d 2 3d = -8d

+8d + 8d 11d = 0 11 11 d = 0

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