How do you factor the expression x^2-10x+24?

1 Answer
Alan P.
Dec 8, 2015

(x-6)(x-4)

Explanation:

We attempt to generate factors in the form:
color(white)("XXX")(x+a)(x+b)

Since the constant term: +24 is positive
we know that a and b have the same sign.

Since the middle term: (-10x) is negative
we know that a and b are negative.

All that remains is to find factors of 24
that add up to 10

Factors of 24
color(white)("XXX"){(1,24), (2,12), (3,8), (4,6)}

Only the factors (4,6) add up to 10

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