This document discusses factoring special polynomials, including perfect square polynomials and the difference of two squares. Perfect square polynomials have a first term and last term that are perfect squares, and the middle term is twice the product of the square roots of the first and last terms. The difference of two squares can be factored by taking the square root of the first term and finding the positive and negative factors of the last term.

1. Factoring Special Polynomials Holt Text pages 452-454

2. Perfect Square Polynomials Examples (x+2) 2 (x-3) 2

3. Terminology Perfect Square Polynomials First term is a perfect square Last term is also a perfect square Middle Term: Multiply the square root of the first and last terms, then double it. Is x 2 + 12x + 36 a perfect square polynomial?

4. x 2 +8 x+16 What is the square root of: x 2 ? 16? What is 2(x)(4)? Is x 2 +8 x+16 a perfect square.

5. 3x 2 +3 x+16 What is the square root of: 3x 2 ? 16? Is 3 x 2 +16 x+16 a perfect square?

6. x 2 +3 x+9 What is the square root of: x 2 ? 16? What is 2(x)(4)? Is x 2 +8 x+16 a perfect square?

7. Factor 9x 2 +24 x+16 Since the sq. root of 9x 2 is 3x Since the sq. root of 16 is 4 (3x+4) 2 equals the above polynomial.

8. Factor 64x 4 -16 x 2 y+y 2 Since the sq. root of 64x 4 is 3x Since the sq. root of y 2 is 4 (8x 2 +y) 2 equals the above polynomial.

9. Difference of Two Squares Factor 4x 2 -25 Negative constants have a negative and positive factor Positive square numbers have two positive factors

10. Factor 4x 2 -25 The square root of the first term: 4x The positive and negative factors of -25 are -5 and +5 This converts to (2x-5)(2x+5) Notice the only difference between the difference of two squares and (2x+5)(2x+5).

11. Factor 16x 2 -49 The square root of the first term: 4x The positive and negative factors of -49 are -7 and +7 This converts to (4x-7)(4x+7)

12. Factor x 2 -4 The square root of the first term: x The positive and negative factors of -49 are -2 and +2 This converts to (x-2)(x+2)

13. Factor 81x 2 -64 The square root of the first term: 9x The positive and negative factors of -64 are -8 and +8 This converts to (9x-8)(9x+8)