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

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

Using the FOIL Method to Multiply Binomials Multiplying Polynomials - FOIL Using the FOIL Method to Multiply Binomials 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

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

Multiplying Polynomials – Special Formulas The Square of a Binomial Sum The Square of a Binomial Difference The Product of the Sum and Difference of Two Terms Blitzer, Algebra for College Students, 6e – Slide #7 Section 5.2

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

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

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

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

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

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

Multiplying Polynomial Functions EXAMPLE SOLUTION To find f (a + h) – f (a), we first replace each occurrence of x with a + h and then replace each occurrence of x with a. Then we perform the resulting operations and simplify. f (a + h) – f (a) Use , replacing x with a + h and a, respectively. Blitzer, Algebra for College Students, 6e – Slide #14 Section 5.2

Multiplying Polynomial Functions CONTINUED Multiply as indicated Multiply Combine like terms Blitzer, Algebra for College Students, 6e – Slide #15 Section 5.2