1. Factoring GCF, Monics, Solving Monics

2. Quadratics Solve x 2 – 8x + 15 = 0 by using the following graph.

3. Factoring - Concept Factoring Distributive Property ab+ac Factoring a(b+c) Greatest Common Factor?

4. Identifying GCF in Terms What is the GCF: 2x 3 y, 4x 2 y 3 Find the GCF of the coefficients is: Find the GCF of the first variable: Find the GCF of the 2 nd variable: Combine to form total GCF: GCF is the greatest combination of factors that divide into both terms evenly. If the polynomial was 2x 3 y + 4x 2 y 3, how could we factor this? GCF( + ) ( + ) Check: redistribute!

5. Factoring GCF Examples Factor: 15x 2 y 5 + 20xy 3 GCF: 5xy 3 Divide out GCF from each term and rewrite as product: Answer: 5xy 3 (3xy 2 + 4)

6. Factoring GCF Examples Factor: 32x 2 y 2 + 16x 2 y 3 GCF: 16x 2 y 2 Divide out GCF from each term and rewrite as product: Answer: 16x 2 y 2 (2 + y)

7. Factoring GCF Examples Factor: 2x(a – b) + 4y(a – b) GCF: (a - b) Divide out GCF from each term and rewrite as product: Answer: (a – b)(2x + 4y)

8. Factoring Monics Monic: Quadratic polynomial with an x 2 coefficient of 1. Examples: x 2 + 3x + 2, x 2 + 5x + 6, x 2 - 6x + 9 Helpful Hint: If you multiply (x + 1)(x + 2), what do you get? So, factoring quadratics yields 2 binomial factors.

9. Factoring Monics Factor: x 2 + 3x + 2 1 st : Look at the constant in your polynomial. 2 nd : Find factor pairs for that constant 3 rd : Look at the 2 nd sign in your polynomial If the second sign is positive, the signs in your binomials will be the same (The sign of the x coefficient). Find factor pairs for the constant that add up to the coefficient of the x term. If the sign is negative, the signs in your binomials will be different. Find factor pairs for the constant whose difference is the coefficient of the x term. 4 th : Write your factors. 5 th : Check by multiplying/distributing.

10. Factoring Monics Factor: x 2 + 5x - 6 1 st : Look at the constant in your polynomial. 2 nd : Find factor pairs for that constant 3 rd : Look at the 2 nd sign in your polynomial If the second sign is positive, the signs in your binomials will be the same (The sign of the x coefficient). Find factor pairs for the constant that add up to the coefficient of the x term. If the sign is negative, the signs in your binomials will be different. Find factor pairs for the constant whose difference is the coefficient of the x term. 4 th : Write your factors. 5 th : Check by multiplying/distributing.

11. Factoring Monics Factor: x 2 - 4x - 12 1 st : Look at the sign of the constant in your polynomial. 2 nd : Find factor pairs for that constant 3 rd : Look at the 2 nd sign in your polynomial If the second sign is positive, the signs in your binomials will be the same (The sign of the x coefficient). Find factor pairs for the constant that add up to the coefficient of the x term. If the sign is negative, the signs in your binomials will be different. Find factor pairs for the constant whose difference is the coefficient of the x term. 4 th : Write your factors. 5 th : Check by multiplying/distributing.

12. Solving Monics …or any quadratic, for that matter… Zero Product Rule: If two numbers multiplied together equal zero, than either the first number or the second number must be zero. If ab = 0, then either a = 0 or b = 0 Applying Zero Product Rule to Factors: Solve: x 2 + 3x + 2 = 0 Factor: (x + 2)(x + 1) = 0 (do you see two things being multiplied?) Set Factors Equal to zero & Solve: x + 2 = 0 or x + 1 = 0

13. Practice Solving x 2 + 5x + 6 = 0 Answer: x = -3, -2 x 2 + 5x - 12 = 0 Answer: x = -6, 1 x 2 - 6x + 9 = 0 Answer: x = 3 x 2 - 3x - 4 = 0 Answer: x = -1, 4

14. Homework Factoring Worksheet