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Factoring Review
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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
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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!
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Finding Factors of C Identify the value of c
On your calculator, go to the y= screen Type C/X into y1 Go to the table Any whole numbers (positive, non-decimal numbers) in the y1 column are factors of c
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Example
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Example #1
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Example #2
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Example #3
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Your Turn: Complete problems 1 – 3 on the “Factoring Practice” handout
Check your answer by FOIL-ing!
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1. (x + 9)(x + 2) 2. (y – 7)(y + 5) 3. (g – 6)(g + 2)
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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)
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Example #1
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Example #2
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Your Turn: Complete problems 4 – 10 on the “Factoring Practice” handout Remember to check your answer by FOIL-ing!
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Factoring (when a ≠ 1): The Welsh Method
Multiply c and a Rewrite the expression with the new value for c Write (ax + )(ax + ) Finish “factoring” the new expression Reduce each set of parentheses by any common factors
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Example #1
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Example #2
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Example #3
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Your Turn: Complete problems 11 – 20 on the “Factoring Practice” handout Don’t forget to check by FOIL-ing!
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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
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GCF (Greatest Common Factor)
Steps: Identify any common factor(s) (including the GCF) Factor out the common factor(s) Factor the remaining expression if possible
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Example #1
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Example #2
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Example #3
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Your Turn: Complete problems 17 – 27 on “Factoring Practice” handout
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Warm-up (2 m) 20x6y7 + 12xy3 + 28x7y2 6x2 + 19x - 11
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GCFs and The Welsh Method
Make sure you factor out any GCFs or the Welsh Method doesn’t work!!!
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Your Turn: Complete problems 28 – 33 on the “Factoring Practice” handout using the GCF and the Welsh Method
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Picking the Correct Method
34. x2 + 10x + 16
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Picking the Correct Method
35. 5t2 + 28t + 32
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Picking the Correct Method
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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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