Chapter 6 Section 4

Special Factoring Techniques 6.4 Special Factoring Techniques Factor a difference of squares. Factor a perfect square trinomial. 2 3 4

Special Factoring Techniques By reversing the rules for multiplication of binomials from Section 5.6, we get rules for factoring polynomials in certain forms. Slide 6.4-3

Factor a difference of squares. Objective 1 Factor a difference of squares. Slide 6.4-4

Factor a difference of squares. The formula for the product of the sum and difference of the same two terms is Factoring a Difference of Squares For example, The following conditions must be true for a binomial to be a difference of squares: 1. Both terms of the binomial must be squares, such as x2, 9y2, 25, 1, m4. 2. The second terms of the binomials must have different signs (one positive and one negative). Slide 6.4-5

Factoring Differences of Squares EXAMPLE 1 Factoring Differences of Squares Factor each binomial if possible. Solution: After any common factor is removed, a sum of squares cannot be factored. Slide 6.4-6

Factoring Differences of Squares EXAMPLE 2 Factoring Differences of Squares Factor each difference of squares. Solution: You should always check a factored form by multiplying. Slide 6.4-7

Factoring More Complex Differences of Squares EXAMPLE 3 Factoring More Complex Differences of Squares Factor completely. Solution: Factor again when any of the factors is a difference of squares as in the last problem. Check by multiplying. Slide 6.4-8

Factor a perfect square trinomial. Objective 2 Factor a perfect square trinomial. Slide 6.4-9

Factor a perfect square trinomial. The expressions 144, 4x2, and 81m6 are called perfect squares because A perfect square trinomial is a trinomial that is the square of a binomial. A necessary condition for a trinomial to be a perfect square is that two of its terms be perfect squares. Even if two of the terms are perfect squares, the trinomial may not be a perfect square trinomial. and Factoring Perfect Square Trinomials Slide 6.4-10

Factoring a Perfect Square Trinomial EXAMPLE 4 Factoring a Perfect Square Trinomial Factor k2 + 20k + 100. Solution: Check : Slide 6.4-11

Factoring Perfect Square Trinomials EXAMPLE 5 Factoring Perfect Square Trinomials Factor each trinomial. Solution: Slide 6.4-12