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Polynomial and Monomial Multiplication Methods

Learn to multiply polynomials by monomials using the distributive property through horizontal and vertical methods. Simplify expressions and solve polynomial equations involving distribution.

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Polynomial and Monomial Multiplication Methods

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  1. 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

  2. The Distributive Property • Method 1: Horizontal -2x2(3x2 – 7x + 10) -2x2(3x2)–2x2(-7x)– 2x2(10) - 6x4 + 14x3 – 20x2

  3. Method 2: Vertical • 3x2 – 7x + 10 x - 2x2 -6x4 + 14x3 – 20x2

  4. Simplify Expressions • 4(3d2 + 5d)–d(d2 -7d + 12) • 12d2 + 20d –d3 + 7d2 – 12d • group like terms • - d3 + (12d2 + 7d2) + (20d – 12d) • add like terms • -d3 + 19d2 + 8d

  5. Polynomial equations d(d-1) + 4d = d(d-8) Distribute d2 – d + 4d = d2 – 8d Combine like terms d2 + 3d = d2 – 8d

  6. d2 + 3d = d2 – 8d • Now solve for d d2 + 3d = d2 – 8d • d2 - d2 3d = -8d

  7. 3d = -8d 3d = -8d +8d + 8d 11d = 0 11 11 d = 0

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