FACTORING

Common Factor Approach

4xy^2  - 16x^3 y^2

4xy^2  (1 - 4x^2)

x^2 - 8x + 12

If we have ax^2 + bx + c

Factoring always begins with finding two numbers whose sum is b and whose product is ac.

a = 1   b = -8    c = 12

Can you think of two numbers whose product is (1)(12) = 12   and whose sum is -8?

(x-6)(x-2)

x^2 - 6x -2x + 12

x (x-6)  -2 (x-6)

(x-2)(x-6)

x^2 + 2x - 15

(x+5)(x-3)

x^2 + 18x + 81

(x+9)(x+9) = (x+9)^2

x^2 - 169

(x-13)(x+13)

x^2 + 0x - 169


2x^2 +9x - 5

ac = -10  b = 9

10 -1  Now divide by a

5  -1/2

  2(x+5)(x-1/2)

(x+5)(2x-1)


Factoring ax^2 + bx + c

1.  Find two numbers whose sum is b and whose product is ac.
2.  Divide both those numbers by a.
3.  Make factors a(x+number1)(x+number2).
4.  Move a into parentheses to remove fractions if you want.


Factor 6x^2 + x - 2

1.  Find two numbers whose sum is 1 and whose product is -12
    -3   4

2.  Divide -3 and 4 by 6
    -3/6      4/6
    -1/2      2/3

3   6(x-1/2)(x+2/3)
    2(x-1/2)  3(x+2/3)
    (2x-1)(3x+2)


4x^2 + 21x + 20

ac = 80    b = 21

16  5

4   5/4

4(x+4)(x+5/4)

(x+4) 4(x+5/4)

(x+4) (4x+5)