Can this be written in factored form?

Question

My equation is -x^2+24x+168. I have to write it in factored form but I can’t find the factored pair of -168 that equals -24

Answer 1

"-x^2 + 24x + 168" is not factorable: it does not have integer roots.

It can be solved by the quadratic formula.

For your reference, roots are x = -5.664 and x = 29.664

Answer 2

if you can't find the factors through trial and error, either complete the square or use the quadratic formula. IF the answer is in integers, then you can find the factors

-x^2 + 24x + 168 =0

multiply by -1

change the signs

x^2 -24x -168 = 0

x^2 -24x + 144 = 168 + 144 = 312

(x-12)^2 = 312

x-12 = sqr312 = 17.664 which suggests you can't factor the problem with integers

x = 12+ or - sqr312

then the factors are (x-12+sqr312)(x-12-sqr312)

their product is x^2 -24x + 144 -312 = x^2 -24 -168

change the signs and you're back to the original polynomial -x^2 +24 + 168

they aren't integer factors, but they are real, not imaginary

change the sign of one of the factors to get a product of factors = original polynomial