Factoring Review

25 January 2011

Factoring The process of rewriting an

equation or expression as the product of its factors

Example: x2 + 3x + 2 = (x + 2)(x + 1)

Most common form is the quadratic form: ax2 + bx + c, a ≠ 0

Factoring (when a = 1)ax2 + 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 C1. Identify the value of c2. On your calculator, go to the y=

screen3. Type C/X into y14. Go to the table5. Any whole numbers (positive,

non-decimal numbers) in the y1 column are factors of c

Example

Example #1

24x11x2

Example #2

35x2x2

Example #3

12x7x2

Your Turn: Complete problems 1 – 4 on the

“Factoring Practice” handout Check your answer by FOIL-ing!

Difference of Squares When we use it:

Usually in the form ax2 – c Both a and c are perfect squares (the

square root of each number is a whole number)

)cxa)(cxa(

cax2

Example #1

81h2

Example #2

144j49 2

Your Turn: Complete problems 5 – 10 on the

“Factoring Practice” handout Remember to check your answer

by FOIL-ing!

Factoring (when a ≠ 1):The Welsh Method Pt. I

1. Multiply c and a2. Rewrite the expression with the new

value for c3. Write (ax + )(ax + )4. Finish “factoring” the new expression5. Reduce each set of parentheses by

any common factors

Example #14y13y3 2

Example #22x5x3 2

Example #32g5g7 2

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: when the all the

terms share 1 or more factors Factoring out GCFs save us

time!!!

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 #1x3x2x 23

Example #264x32x4 2

Example #3234 y21y24y3

Your Turn: Complete problems 1 – 10 on

“Functions Practice Pt. II” handout

GCFs and The Welsh Method

20x14x2 2 Make sure you factor out any

GCFs or the Welsh Method

doesn’t work!!!

Your Turn: Complete problems 11 – 22 on the

“Factoring Practice Part II” handout