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 bYou 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
Your Turn: Complete problems 1 – 3 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
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 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
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!!!
4x2 – 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
GCFs and The Welsh Method
4x14x12 2 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
Your Turn: Completely factor problems 36 – 44 on the
“Factoring Practice” handout. In your solution, state the method(s) you used to completely factor the expression.
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