Expert: Sherman D. - 12/3/2007

Question
x^2 + 1x - 56

Answer
right of hand i know this answer is (x + 8)(x - 7), because 8 * 7 = 56, and 8 - 7 = +1. By the way, when you have a 1x, you can just right it as x.

here is the best way to figure out how to factor a problem.

when given a problem in ax^2 + bx + c = 0 form, your formula to find the x values is

x = (-b ± sqrt(b^2 - 4ac))/(2a)

x = (-1 ± sqrt(1^2 - 4(1)(-56)))/(2(1))
x = (-1 ± sqrt(1 + 224))/2
x = (-1 ± sqrt(225))/2
x = (-1 ± 15)/2
x = (-16/2) or (14/2)
x = -8 or 7

now whenever you have the values of x, the formula is

(dx - e)(fx - g)
where a and c are the denominator, and b and d are the numerators, so in our case.

so

since we have x = -8 or 7, which is the same thing as saying -8/1 or 7/1

we can write the factored form as

(1x - (-8))(1x - 7)

which can be rewritten as

(x + 8)(x - 7)

and there you have it.