How do you find the factors of a polynomial?

Answer 1

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