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§ 5.2

§ 5.2. Multiplication of Polynomials. Multiplying Polynomials. EXAMPLE. Multiply. SOLUTION. Rearrange factors. Multiply coefficients and. add exponents. Simplify. Blitzer, Algebra for College Students, 6e – Slide # 2 Section 5.2. Multiplying Polynomials. EXAMPLE. Multiply.

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§ 5.2

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  1. §5.2 Multiplication of Polynomials

  2. Multiplying Polynomials EXAMPLE Multiply SOLUTION Rearrange factors Multiply coefficients and add exponents Simplify Blitzer, Algebra for College Students, 6e – Slide #2 Section 5.2

  3. Multiplying Polynomials EXAMPLE Multiply SOLUTION Distribute Multiply coefficients and add exponents Blitzer, Algebra for College Students, 6e – Slide #3 Section 5.2

  4. Multiplying Polynomials EXAMPLE Note this: We multiply each term of the binomial by each term of the trinomial. We get 6 products in all. Multiply SOLUTION Multiply the trinomial by each term of the binomial Distribute Multiply coefficients and add exponents Simplify Blitzer, Algebra for College Students, 6e – Slide #4 Section 5.2

  5. Multiplying Polynomials - FOIL last F O I L first inside Product of First terms Product of Outside terms Product of Inside terms Product of Last terms outside Blitzer, Algebra for College Students, 6e – Slide #5 Section 5.2

  6. Multiplying Polynomials - FOIL EXAMPLE Multiply SOLUTION last F O I L first Multiply inside outside Combine like terms Blitzer, Algebra for College Students, 6e – Slide #6 Section 5.2

  7. Multiplying Polynomials – Special Formulas Blitzer, Algebra for College Students, 6e – Slide #7 Section 5.2

  8. Multiplying Polynomials – Special Formulas EXAMPLE Multiply SOLUTION Use the special-product formula shown. Blitzer, Algebra for College Students, 6e – Slide #8 Section 5.2

  9. Multiplying Polynomials – Special Formulas EXAMPLE Multiply SOLUTION Use the special-product formula shown. Blitzer, Algebra for College Students, 6e – Slide #9 Section 5.2

  10. Multiplying Polynomials – Special Formulas EXAMPLE Multiply SOLUTION Use the special-product formula shown. - = First Term Squared Second Term Squared Product = Blitzer, Algebra for College Students, 6e – Slide #10 Section 5.2

  11. Multiplying Polynomials – Special Formulas EXAMPLE Multiply SOLUTION We can group the terms so that the formula for the square of a binomial can be applied. (A + B) (A - B) =- Blitzer, Algebra for College Students, 6e – Slide #11 Section 5.2

  12. Multiplying Polynomial Functions EXAMPLE (a) (fg)(x) (b) (fg)(-1) (c) (fg)(0) SOLUTION (a) (fg)(x) = f(x) g(x) Thus, = (x - 4)(x + 10) F O I L Blitzer, Algebra for College Students, 6e – Slide #12 Section 5.2

  13. Multiplying Polynomial Functions CONTINUED (b) We use the product function to find (fg)(-1) – that is, the value of the function fg at -1. Replace x with -1. (c) We use the product function to find (fg)(0) – that is, the value of the function fg at 0. Replace x with 0. Blitzer, Algebra for College Students, 6e – Slide #13 Section 5.2

  14. 5.2 Assignment p.327 (2-8 even, 14-32 even, 40-50 even, 56, 58, 70, 72, 95, 96)

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