Question

Solve by factoring x^2 plus 8x ,minus 20 equal 0

Answer 1

x^2 + 8x - 20 = 0

(x + 10) (x-2) = 0

x = -10, 2

Answer 2

All terms must be multiplied for factoring.

x^2 + 8x - 20 = 0
Start by putting an x as the front of each term.

(x _)(x _) = 0
When FOILing, we know that the "last" has to be a -20, so one sign is negative, and the other is positive.

(x + _)(x - _) = 0
When multiplied, the two blanks have to equal -20. We could have 20 and 1, 10 and 2, 5 and 4 (with one of the numbers being negative.)

Well, one of the negatives plus the positive has to equal 8... so 10 and 2 are what we want.

(x + 2)(x - 10) = 0
Check by foiling.

x^2 - 10x + 2x - 20 = 0
x^2 - 8x - 20 = 0

That's not our original expression, so the signs need to be switched.

(x - 2)(x + 10) = 0
Check again.

x^2 + 10x - 2x - 20 = 0
x^2 + 8x - 20 = 0

That's what we want, so (x-2)(x+10) is the answer.

Answer 3

Oh, and to solve, set each term equal to 0.
x - 2 = 0, x + 10 = 0
x = 2, x = -10