Factoring Polynomials
How to Factor Trinomials in the form of ax2 + bx + c
Step 1:
Are there any common factors? If so, factor them out.
Step 2:
How many terms are in the polynomial?
A. If there are Two terms, decide if one of the following can be applied
1. Difference of two Squares:
2. Difference of two Cubes:
3. Sum of two cubes:
B.
C.
If there are Three terms, try one of the following.
1. Perfect Square Trinomial a2 + 2ab + b2 = (a + b)2
2. Perfect Square Trinomial a2 − 2ab + b2 = (a − b)2
3. If not a perfect square trinomial, then try using the Fraction Method
If there are Four terms, try factoring by grouping.
Factoring Trinomials in the form of ax2 + bx + c
Fraction Method
EXAMPLE:
2 x  9 x  18
2
Step 1:
Copy the trinomial into an expression: a fraction with two binomials with the leading coefficient in both quantities divided by that coefficient: (2 x
)(2x
)
2
Step 2:
Multiply the leading coefficients by the last number in the trinomial: 2 X 18 = 36 Step 3:
Find Factors of 36 that yield the middle value when added or subtracted. Hint! The last sign tells us to subtract the factors. ___________ 36________
In this example the two factors are 3 and ‐12 1  36, 2  18, 3 12, 4  9, 6.6,
Step 4:
The two factors are substituted into the original expression: (2 x -12)(2x  3)
Step 5:
Factor the common number(s) and reduce the numbers: 2( x  6)(2 x  3)
2
2
Step 6:
The remaining factors are the answer to the trinomial factorization: ( x  6)(2 x  3)
Step 7:
Check! Multiply the binomials. If your factors are correct, you should get the original trinomial. Foil
( x  6)(2 x  3)
2 x 2  3 x  12 x  18
2 x 2  9 x  18
saved: Math Handout (Factoring) 2
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