Factoring Review
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Transcript of Factoring Review
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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 bYou can always check your answer by
FOIL-ing!
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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
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Example
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Example #1
24x11x2
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Example #2
35x2x2
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Example #3
12x7x2
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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)
)cxa)(cxa(
cax2
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Example #1
81h2
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Example #2
144j49 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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4. 5.
6. 7.
8.
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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
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Example #1
4y13y3 2
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Example #2
2x5x3 2
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Example #3
2g5g7 2
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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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11. 12.
13. 14.
15. 16.
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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:1. Identify any common factor(s) (including
the GCF)2. Factor out the common factor(s)3. Factor the remaining expression if possible
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Example #1
x3x2x 23
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Example #2
64x32x4 2
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Example #3234 y21y24y3
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Your Turn: Complete problems 17 – 27 on “Factoring
Practice” handout
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17. 18.
19. 20.
21. 22.
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23. 24.
25. 26.
27.
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GCFs and The Welsh Method
20x14x4 2 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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28. 29.
30. 31.
32. 33.
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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
36. 27p2 – 9p
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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.
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37. 38.
39. 40.
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41. 42.
43. 44.