2 4 part 1 Basic Factoring I can

2. 4 part 1 - Basic Factoring I can. . . - Factor using GCF -Factor a difference of two perfect squares -Factor basic trinomials

Difference of Two Perfect Squares When a quadratic is in the form: ax 2 – c ; b = 0, c is negative, and a and c are perfect squares (ex: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121…) To Factor: 1. Square root the first item and place in the first spot of each parenthesis. 2. Square root the second term and place in the second spot in each parenthesis. Example: 4 x 2 – 9 (2 x + 3)(2 x – 3)

To Factor and Expression in the Form: ax 2 + bx + c when a=1 Put the equation in standard form FIRST (highest exponent to lowest) Look to see if you can factor out the GCF (a common factor in ALL terms) Look to see if you can factor using the difference of two perfect squares. Look to see what two numbers multiply to get (c) and add to get (b) These two numbers are placed in the parenthesis (x +/- ____) FOIL to check

Examples: Factor each expression completely. 1. 5 x 2 + 30 x The GCF is 5 x, so: 5 x(x + 6) 2. 15 y 2 – 10 y The GCF is 5 y, so: 5 y(3 y – 2) 3. 5 rs 2 + 20 r 2 s The GCF is 5 rs, so: 5 rs(s + 4 r)

4. x 2 – 81 (x + 9)(x – 9) 5. 9 x 2 – 25 (3 x – 5)(3 x + 5) 6. 3 x 2 – 48 The GCF is 3 so we need to factor that out first: 3(x 2 – 16) 3(x + 4)(x – 4) 7. 2 x 2 – 2 The GCF is 2 so we need to factor that out first: 2(x 2 – 1) 2(x + 1)(x – 1)

8. -15 + 2 x + x 2 First write in standard form: x 2 + 2 x – 15 What multiplies to get -15 AND adds to 2? 5 and -3 So to factor we write our two parenthesis: (x + 5)(x – 3)

9. 36 – 5 x – x 2 Standard form: -x 2 – 5 x + 36 Factor out the (-), so –(x 2 + 5 x – 36) Now factor, what multiplies to -36 and adds to 5? 9 and -4 -(x + 9)(x – 4)

10. 30 + 5 x – 5 x 2 Standard form: -5 x 2 + 5 x + 30 Factor out the GCF: -5 -5(x 2 – x – 6) Factor, what multiplies to -6 and adds to -1? -3 and 2 -5(x – 3)(x + 2)