Algebra Demystified 2nd Ed

156 algebra De mystif ieD

consider 1 and 12, 2 and 6, and 3 and 4. If both signs in the factors are the same,

these are the only ones we need to try. If the signs are different, we need to

reverse the order: 1 and 12, as well as 12 and 1; 2 and 6, as well as 6 and 2; 3

and 4, as well as 4 and 3. We try the FOIL method on these pairs. (Not every

quadratic polynomial can be factored in this way.)

EXAMPLE

Write the possible factors, and then check to see which of them are the

correct factors.

x^2 + x – 12 [Factors to check: (x + 1)(x – 12), (x – 1)(x + 12), (x + 2)(x – 6),

(x – 2)(x + 6), (x – 4)(x + 3) and (x + 4)(x – 3)]

(x + 1)(x – 12) = x^2 – 11x – 12

(x – 1)(x + 12) = x^2 + 11x – 12

(x + 2)(x – 6) = x^2 – 4x – 12

(x – 2)(x + 6) = x^2 + 4x – 12

(x – 4)(x + 3) = x^2 – x – 12

(x + 4)(x – 3) = x^2 + x – 12 (This works.)

EXAMPLES

x^2 – 2x – 15 Factors to check: (x + 15)(x – 1), (x – 15)(x + 1), (x + 5)(x – 3)

and (x – 5)(x + 3) (This works)

x^2 – 11x + 18 Factors to check: (x – 1)(x – 18), (x – 3)(x – 6) and (x – 2)(x – 9)

(This works)

x^2 + 8x + 7 Factors to check: (x + 1)(x + 7) (This works)

PRACTICE

Factor the expression.

1. x^2 − 5x − 6 =


2. x^2 + 2x + 1 =


3. x^2 + 3x − 10 =


4. x^2 − 6x + 8 =


5. x^2 − 11x − 12 =


6. x^2 − 9x + 14 =


7. x^2 + 7 x + 10 =

EXAMPLE

Write the possible factors, and then check to see which of them are the

EXAMPLES

xxx^22

PRACTICE

Factor the expression.