Factoring Review

Factoring The process of rewriting an equation or expression as the product of its factors Example: x 2 + 3x + 2 = (x + 2)(x + 1) Most common form is the quadratic form: ax 2 + bx + c, a ≠ 0

Factoring (when a = 1) ax 2 + bx + c = (x + ___ ) (x + ___ ) multiply to equal c and add up to equal b You can always check your answer by FOIL-ing!

Finding Factors of C 1. Identify the value of c 2. On your calculator, go to the y= screen 3. Type C/X into y1 4. Go to the table 5. Any whole numbers (positive, non- decimal numbers) in the y1 column are factors of c

Example

Example #1

Example #2

Example #3

Your Turn: Complete problems 1 – 3 on the “Factoring Practice” handout Check your answer by FOIL-ing!

1. (x + 9)(x + 2) 2. (y – 7)(y + 5) 3. (g – 6)(g + 2)

Difference of Squares When we use it: Usually in the form ax 2 – c Both a and c are perfect squares (the square root of each number is a whole number)

Example #1

Example #2

Your Turn: Complete problems 4 – 10 on the “Factoring Practice” handout Remember to check your answer by FOIL-ing!

Factoring (when a ≠ 1): The Welsh Method 1. Multiply c and a 2. Rewrite the expression with the new value for c 3. Write (ax + )(ax + ) 4. Finish “factoring” the new expression 5. Reduce each set of parentheses by any common factors

Example #1

Example #2

Example #3

Your Turn: Complete problems 11 – 20 on the “Factoring Practice” handout Don’t forget to check by FOIL-ing!

GCF (Greatest Common Factor) When we use it: all the terms share 1 or more factors Factoring out GCFs save us time!!! 4x 2 – 196 = 0 (2x + 14)(2x – 14) = 0

GCF (Greatest Common Factor) Steps: 1. Identify any common factor(s) (including the GCF) 2. Factor out the common factor(s) 3. Factor the remaining expression if possible

Example #1

Example #2

Example #3

Your Turn: Complete problems 17 – 27 on “Factoring Practice” handout

GCFs and The Welsh Method Make sure you factor out any GCFs or the Welsh Method doesn’t work!!!

Your Turn: Complete problems 28 – 33 on the “Factoring Practice” handout using the GCF and the Welsh Method

Picking the Correct Method 34. x x + 16

Picking the Correct Method 35. 5t t + 32

Picking the Correct Method p 2 – 9p

Your Turn: Completely factor problems 37 – 44 on the “Factoring Practice” handout. In your solution, state the method(s) you used to completely factor the expression.