Factoring trinomials:
ax2 + bx + c
The process of factoring a trinomial is finding two binomials whose product is the given trinomial.
Method 1 - Reverse FOIL Method – Look for two binomials that will result in the given trinomial when
you multiplied. This is easier when a=1, but can get complicated with the leading coefficient being
something other than one.
In all methods, you must find the factors of the product of a and c, that add to b.
Method 2
for 𝟔𝒙𝟐 + 𝒙 − 𝟏𝟐
Step 1: Multiply the first and last terms
(6x2)(-12)= -72x2
Step 2: Find factors of -72 that will subtract or add to make +1 (coefficient of the middle term)
9x and -8x
Step 3: Replace the middle term with 9x and -8x
6x2 + 9x – 8x – 12
Step 4: Factor out the Greatest Common Factor from the 1st and 2nd terms and then from the 3rd and 4th
terms
6x2 + 9x – 8x – 12
3x(2x + 3) – 4(2x + 3)
works like 5a – 3a = (5 – 3)(a) = 2a
Step 5: Combine like terms (Final Answer)
(3x – 4)(2x + 3)
Step 6: Check to be sure it works … FOIL.
6x2 + 9x – 8x – 12 =
𝟔𝒙𝟐 + 𝒙 − 𝟏𝟐 
Method 3
GCF, Slide and Divide
for 16x2 + 20x – 6
1. Be sure to pull out any GCF! You will not get a correct set of factors if
you forget.
2. “Slide a” to end, and multiply a ∙ c.
3. Factor like before … find factors of ac that add to b.
4. Write binomials.
5. Divide both constants by the number you slid out of the way (a).
6. Simplify the two fractions.
7. Once they are simplified, if there’s a fraction left, the denominator
becomes the coefficient of the variable term.
For a video, see … https://www.youtube.com/watch?v=s_4wAP1tulU
Method 4
for ax2 + bx + c
Tic-Tac-Toe Factoring:
The tic-tac-toe will not do the factoring for you. But it
will keep everything organized so you can concentrate on the
numbers.
1. Put ax2 and c in boxes #1 & 2, and b in box #10.
2. Write factors of acx2 that add to bx in boxes #6 and 9.
3. Write factors of ax2 in boxes #4 & 7and factors of c in boxes #5 & 8,
that are also factors of box #6 in boxes #4 & 5 and factors of box #9 in boxes
#7 & 8.
4. The binomial factors can be found by using the diagonal pairs of boxes #4 &
8, and #7 & 5.
… now with numbers …
for 8x2 + 10x – 3
1
Tic-Tac-Toe Factoring:
5.1. The
tic-tac-toe will not do the factoring for you. But it
Put 8x2 and -3 in boxes #1 & 2, and 10 in box #10.
will keep everything organized so you can concentrate on the
2. numbers.
Write factors of -24x2 that add to 10x in boxes #6 and 9.
6.3. Write factors of 8x2 in boxes #4 & 7and factors of -3 in boxes #5 & 8,
1.
that are also factors of box #6 in boxes #4 & 5 and factors of box #9 in
boxes #7 & 8.
2
8x2
-3
4
5
6
7
8
9
(
-24x2
10x
10
4. The binomial factors can be found by using the diagonal pairs of boxes
#4 & 8, and #7 & 5.
Answer -
3
1
)(
)
For a great slide show, see… http://www.scribd.com/doc/2440412/Tic-Tac-Toe-Factoring.
Method 5
Fraction Factoring:
This method will not factor for you either, but it is another method to keep your thinking organized.
for ax2 + bx + c
1. Factor out GCF. This must be done first with this method!
2. Multiply a ∙ c.
3. Find factors of ac that add to b.
factor and factor
4. Write those factors as numerators of fractions with a as the denominator
a
a
5. Simplify the two fractions.
6. The binomial factors can be found by using the fractions’ denominators as the coefficients of x for the
first term, and the numerators as the second term.
… now with numbers …
7.
1.
2.
3.
4.
5.
for 8x2 + 10x – 3
Factor out GCF. This must be done first with this method!
Multiply 8 ∙ -3.
Find factors of -24 that add to 10.
12 and -2
Write those factors as numerators of fractions with a as the denominator.
8
8
Simplify the two fractions.
The binomial factors can be found by using the fractions’ denominators as the 3 and -1
coefficients of x for the first term, and the numerators as the second term.
2
4
(2x + 3) (4x – 1)