3 4 Factoring Polynomials Objectives Use the Factor

3 -4 Factoring Polynomials Objectives Use the Factor Theorem to determine factors of a polynomial. Factor the sum and difference of two cubes. Holt Mc. Dougal Algebra 2

3 -4 Factoring Polynomials Recall that if a number is divided by any of its factors, the remainder is 0. Likewise, if a polynomial is divided by any of its factors, the remainder is 0. The Remainder Theorem states that if a polynomial is divided by (x – a), the remainder is the value of the function at a. So, if (x – a) is a factor of P(x), then P(a) = 0. Holt Mc. Dougal Algebra 2

3 -4 Factoring Polynomials Check It Out! Example 1 Determine whether the given binomial is a factor of the polynomial P(x). a. (x + 2); (4 x 2 – 2 x + 5) Holt Mc. Dougal Algebra 2 b. (3 x – 6); (3 x 4 – 6 x 3 + 6 x 2 + 3 x – 30)

3 -4 Factoring Polynomials You are already familiar with methods for factoring quadratic expressions. You can factor polynomials of higher degrees using many of the same methods you learned in Lesson 5 -3. Holt Mc. Dougal Algebra 2

3 -4 Factoring Polynomials Check It Out! Example 2 a Factor: x 3 – 2 x 2 – 9 x + 18. Holt Mc. Dougal Algebra 2

3 -4 Factoring Polynomials Check It Out! Example 2 b Factor: 2 x 3 + x 2 + 8 x + 4. Holt Mc. Dougal Algebra 2

3 -4 Factoring Polynomials Just as there is a special rule for factoring the difference of two squares, there are special rules for factoring the sum or difference of two cubes. Holt Mc. Dougal Algebra 2

3 -4 Factoring Polynomials Check It Out! Example 3 a Factor the expression. 8 + z 6 Holt Mc. Dougal Algebra 2

3 -4 Factoring Polynomials Check It Out! Example 3 b Factor the expression. 2 x 5 – 16 x 2 Holt Mc. Dougal Algebra 2

3 -4 Factoring Polynomials Check It Out! Example 4 The volume of a rectangular prism is modeled by the function V(x) = x 3 – 8 x 2 + 19 x – 12, which is graphed below. Identify the values of x for which V(x) = 0, then use the graph to factor V(x). Holt Mc. Dougal Algebra 2

3 -4 Factoring Polynomials Check It Out! Example 4 Continued One corresponding factor is (x – 1). Holt Mc. Dougal Algebra 2