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Lesson 8-2 Multiplying and Factoring Polynomials

Lesson 8-2 Multiplying and Factoring Polynomials. Multiplying Polynomials. Multiplying a binomial by a monomial uses the Distribute property. Distribute the 5. Multiplying Polynomials. What is the simpler form of. A. C. B. D. Solution:. ) (7). Multiplying Polynomials.

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Lesson 8-2 Multiplying and Factoring Polynomials

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  1. Lesson 8-2Multiplying and Factoring Polynomials

  2. Multiplying Polynomials Multiplying a binomial by a monomial uses the Distribute property Distribute the 5

  3. Multiplying Polynomials What is the simpler form of A C B D Solution: )(7)

  4. Multiplying Polynomials Multiplying two binomial uses the FOIL Last First Outer Inner

  5. Multiplying Polynomials What is the simpler form of

  6. Multiplying Polynomials Special case – Square of a binomial What is the simpler form of

  7. Factoring Polynomials Factors: When an integer is written as a product of integers, each of the integers in the product is a factor of the original number.

  8. Factoring Polynomials Greatest common factor – largest quantity that is a factor of all the integers or polynomials involved. Example Find the GCF of each list of numbers. • 6, 8 and 46 6 = 2 · 3 8 = 2· 2 · 2 46 = 2·23 So the GCF is 2 • 144, 256 and 300 144 = 2 ·2·2 ·23 · 3 256 = 2·2·2 · 2 · 2 · 2 · 2 · 2 300 = 2·2· 3 · 5 ·5 So the GCF is 2·2= 4.

  9. Factoring Polynomials Find the GCF of each list of terms. • x3 and x7 x3 = x ·x·x x7 = x ·x·x·x ·x·x·x So the GCF is x · x· x = x3 • 6x5 and 4x3 6x5 = 2 · 3 · x · x· x x· x 4x3 = 2 · 2 ·x ·x·x So the GCF is 2·x ·x·x = 2x3

  10. Factoring Polynomials What is the GCF terms of So the GCF is 5 · xor 5x

  11. Factoring Polynomials • Factoring a polynomial reverses the multiplication process. It is writing a polynomial as a product of polynomials. • To factor a polynomial, find the greatest common factor (GCF) of the coefficients and constants and also the GCF of the variables. • Then write the polynomial as a product by factoring outthe GCF from all the terms.

  12. Factoring Polynomials What is the factored form of Step 1 – Factor each term Step 2 – Find the GCF The GCF is Step 3 - Factoring out of the polynomial

  13. Factoring Polynomials What is the factored form of Step 1 – Factor each term Step 2 – Find the GCF The GCF is Step 3 - Factoring out of the polynomial

  14. Factoring Polynomials • Remember that factoring out the GCF from the terms of a polynomial should always be the first step in factoring a polynomial. • This will usually be followed by additional steps in the process.

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