DO NOW 11/12/14 Homework in the basket please Multiply the following polynomials 1. (3x + 1)(3x – 1) 1. (2z – 7)(z + 4) 1. (4a + 2)(6a2 – a + 2) 1. (7r 2 – 6r – 6) (2r – 4)

Factoring Polynomials

Objective SWBAT factor a polynomial

Vocabulary Factor Greatest Common Factor A number or variable that divides evenly into a given term. The largest number or variable that divides evenly into all given terms.

Finding Greatest Common Factors 1. First look at the coefficients and decide if they can be evenly divided by the same number. Find all the factors and choose the largest 2. Identify the smallest exponent on all common variables 3. Common factor goes outside the parenthesis

Review Find the GCF of: 1. 3 and and x and 15x x2 and 20x x 4x 2

Example: Common Factor 1. 9n2 – 24n 3. 7x – y2 – 5y 7. 3x3 + 6x2 – 15x 2. 7p x – x2 y3 + xy

Practice: Common Factor 1. 4w2 + 2w 2. 18x x2 – 8x 4. 6x4 – 18x3 + 12x2

Factoring Polynomials A "quadratic" is a polynomial that looks like "ax2 + bx + c", where "a", "b", and "c" are just numbers. For the easy case of factoring, you will find two numbers that: – multiply to equal the constant term "c“ – And add up to equal "b", the coefficient on the x- term. Example: Factor x2 + 5x + 6

Example: Quadratics 1. x2 + 8x x2 – 17x + 72

Example: Quadratics 3. x2 – x – x2 + 8x + 15

Practice: Quadratics 1. x2 + 6x x2 + 12x x2 + 14x x2 – 6x x2 – 7x x2 – 11x x2 – 14x – x2 + 3x – x2 + 4x – 5