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Steps for factoring trinomials:
Example
20x**3-62x**2-28x
1. Factor out GCF from each term
20x**3-62x**2-28x - 2x(10x**2-31x-14)
2. Multiply First and Last term
10*-14=140
3. Find 2 factors of Step 2 (140) whose sum is the second term (-31)
140=2*2*5*7
-140=-2*70, 2*-70
-140=-5*28, 5*-28
-140=-7*20, 7*-20
-140=-4*35, 4*-35
-140=-10*14, 10*-14
4. Rewrite
2x(10x**2-31x-14) = 2x(10x**2+4x-35x-14)
5. Factor pairs of terms
2x(10x**2+4x-35x-14) = 2x(2x(5x+2)-7(5x+2))
6. Factor
2x(2x(5x+2)-7(5x+2)) = 2x((2x-7)(5x+2))
2x(2x-7)(5x+2)
Special cases
A. ax**2-b, where sqrt(a) and sqrt(b) are both whole numbers
ax**2-b = (sqrt(a)x+sqrt(b))(sqrt(a)x-sqrt(b))
4x**2-81 =(2x-9)(2x+9)
B. x**2+ax+b where b=c*d and a=c+d
x**2+ax+b = (x+c)(x+d)
x**2-8x-105
Factors of 105:
105=3*5*7
-105=-3*35, 3*-35
-105=-5*21, 5*-21
-105=-7*15, 7*-15
x**2-8x-105 = (x+7)(x+-15)
C. x**2+ax+b where b=c**2 and a=2c
x**2+ax+b = (x+c)**2
x**2+8x+16 = (x+4)**2
NOTES:
> b=c*d OR b=-c*-d
> -b=-c*d OR -b=c*-d
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∙ 13y ago
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