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Algebra II Notes
Factoring Part 1
Steps for Factoring Quadratics:
1) Factor out the greatest common factor (GCF) if it is something other than 1.
a. Find the largest number that divides evenly into all of the coefficients.
b. Find variables that appear in every term and factor them out to the lowest exponent.
2) If the expression has two terms (binomial), determine if it is a difference of perfect squares and
can be written in the form:
2
2
 a    b  If so, it can be factored into  a  b  a  b  or  a  b  a  b 
3) If the expression has three terms (trinomial) and is in the form x 2  bx  c , then determine if
there are factors of c whose sum is b. If there are, then those factors can be used to help factor the
trinomial.
4) If the expression has three terms (trinomial) and is in the form ax2 + bx + c, then determine
factors of ax2 and c whose sum is b.
5) To check your answer, you can _______________ and see if the result is the same as __________
Examples: Factor completely. If not factorable, write ‘prime’.
4 x 2  18 x
3x5  7 x3
d 3  81d
5  20y 2
x 2  5 x  24
y 2  y  42
12a 3bd  54a 2b 4c 2
y 4  19 y 2  48
36  x 2 y 2
16b 4  a 4
x 2  49
x 2  7 xy  12 y 2
bx 2  11bx  60b
x 2  12 x  30
7x2 + 29x + 4
3x – 17x + 20
-10x2 + 26x + 12
24x2 + 15x - 12
3x2 + 15x + 18