Review of GCF, Difference of Squares and Trinomial factoring

4. Difference of Squares: 1. Binomial 2. Must be “-” 3. Both terms must be perfect squares 1. 2. 3. a 2 – b 2 = (a + b)(a – b) (2x + 3)(2x – 3) Use the square roots of the terms! (10x + 9)(10x – 9)

5. Factoring Trinomials Two Types: in the form x 2 + bx + c OR ax 2 + bx + c For the form x 2 + bx + c, … Review: Multiply (x + 4)(x + 2) Note: The two numbers in the quantities add up to 6 and multiply to 8. (x + ____)(x + ____) The two numbers must have a sum of “b” and a product of “c”.

6. Factor: 1. 2. 3. 4. (Think of 2 numbers that multiply to 10 and add to 7). (x + 5)(x + 2) Multiply to -16 and add to -6. (x – 8)(x + 2) (Multiply to -24 and add to 10). (x + 12)(x – 2) (Multiply to 34 and add to -35). (x – 34)( X - 1)

7. The first coefficient of 2 must be “split” as well as the last constant of 3 must be “split” so that the “inners” + “outers” = 7 Factoring ax 2 + bx + c: (____X + ____)(____X + ____) The blanks with the x must multiply to 2 The blanks after the “+” must multiply to 3. When you multiply the inners and outers they must add to 7 (2x + 1)(x + 3) Check with FOIL

8. Factor: 1. 2. 3. (4x + 1)(2x – 3) Find factors of 8 and factors of 3 (3x – 1)(2x + 7) (6x + 1 )(x – 10)