• Factoring ax2 + bx + c

Example -- factor 5x2 − x − 22

1.         Multiply the coefficient of quadratic term and the constant

5 ∙ −22 = −110

2.         List factors of the product from #1 that combines to make the coefficient of the linear term.  That is, the factors of  −110 that combines to make  −1.

10 and  −11

3.                  Re-write the original polynomial with the factors from #2 as the coefficients of the linear term.

5x2 + 10x − 11x −  22

4.                  Factor this polynomial by grouping

5x(x + 2) − 11(x + 2)

(5x − 11)(x + 2)

Example  - factor 3x2 +7x + 2

1.         Multiply 3 ∙ 2 =  6

2.         Factors of 6 that combine to equal 7 ---     1  and  6

3.         Rewrite original equation using the terms from 2       3x2 +6x +x + 2

4.         Factor by grouping                   3x(x + 2) + (x + 2)

(3x + 1)(x + 2)

5.         First = 3x2, Outers = 6x,  Inners = x, Lasts = 2        3x2 +7x + 2

Example #2    factor     5x2 − 3x − 2

1.         Multiply 5 ∙ −2 =  −10

2.         Factors of  −10 that combine to equal −3  --       −5 and 2

3.         Rewrite original equation using the terms from #2         5x2 − 5x + 2x − 2

4.         Factor by grouping                   5x(x − 1) +2 (x − 1)

(5x + 2)(x  − 1)

5.         First = 5x2, Outers =  − 5x,  Inners = 2x, Lasts =  − 2            5x2  − 3x  − 2