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Factoring Review
AMT
Step1. Look for GCF and factor it
out to the front
 1. 7x + 49
 2. 8ax – 56a
 3. t2h + 3t
 4. x + x2y + x3y3
 5. 4a 2b2 + 16ab + 12 a
Factoring by grouping (only do this
when there are 4 terms without a
GCF)
 1. Group the first two terms and the
last two terms
 2. Pull out a GCF for each group
 3. The ( ) should be the same
 4. Final answer is the ( ) that are
the same and the GCF’s in the second
(
)
Examples 6-8
 6. x2 + 3x + x + 3
 7. 2x2 + 2x + 3x + 3
 8. 6x2 – 4x – 3x + 2
Solving
 1. Get everything on one side so the
equation is set = 0 then factor just
like you normally would.
 2. Set each factor equal to 0 and
solve for the variable
Examples 9-11
 9. x(x – 8) = 0
 10. x2 – 5x = 0
 11. 3x2 = 6x
Trinomials
 1. Factors of the last term that + or – to
give you the middle term
 2. Last term + and middle term - ( )( - )

Last term + and middle term + ( +
)( + )

Last term – means ( + ) ( - )
 Larger factor goes with the sign of the middle
term
Examples 12-24
 12. t2 + 8t + 12
 13. p2 + 9p + 20
 14. n2 + 3n – 18
 15. y2 – 5y - 6
 16. x2 + 4x -12
 17. w2 – w – 6
 18. x2 – 8x + 15
 19. t2 – 15t + 56
 20. x2 – 6x + 8 = 0
 21. m2 + 5m + 6 = 0
 22. y2 – 2y -24 = 0
 23. h2 + 2h = 35
 24. n2 – 36 = 5n
More Trinomials
 “Beef” it up and “Cut” the fat
 Same rules as earlier but now we
want factors of the product of the first
and last terms.
 Cut out the GCF at the end
Examples 25-35
 25. 2x2 + 5x + 2
 26. 2x2 + 9x – 9
 27. 2x2 + x – 1
 28. 4x2 – 3x – 3
 29. 9x2 + 6x – 8
 30. 3a
2
+ 30a + 63
 31. 2x2 + 7x + 3 = 0
 32. 3x2 – 7x + 2 = 0

 33. 6x2 + 8x + 2 = 0
 34. 9x2 + 18x – 12 = 6x
 35. 10x2 – 15x = 8x – 12
Differences of Squares
 Factor into (
+
)( -
)
 Take the square root of each term
Examples 36-42







36.
37.
38.
39.
40.
41.
42.
1 – 49d2
t2 – 81u2
64x2 – 9y2
20x2 – 5y2
16x2 – 9 = 0
36b2 – 49 = 0
n2 – 9 = 0