How do you factor the expression −4x2+10x+24?

1 Answer
Tanish J.
Dec 30, 2015

(4−x)(4x+6)

Explanation:

I'm going to explain this using the most common method of factorising: by splitting the middle term.

The first step is to multiply the coefficient of x2 with the constant. We get:

−4⋅24=−96

Now, we need to find the pair of factors of −96 whose sum or difference will give us the coefficient of x, i.e., 10.

−96 has the following pairs of factors:

(96,−1),(32,−3),(16,−6),(8,−12),(4,−24) as well as all these pairs with a reversal of signs.

With a quick glance, it's clear that the sum of the factors in the pair (16,−6) is 10.

Great! So now we split the coefficient of middle term (10) as a sum of 16 and −6 as:

−4x2+(16−6)x+24
−4x2+16x−6x+24

Note: It doesn't matter if you reverse the order and split 10x as −6x+16x, you'll get the same result!

Now, we must take out common factors from the first two terms and then the next two terms:

4x(−x+4)+6(−x+4)

Now, we can take (−x+4) to be common, to get:

(−x+4)(4x+6)

or, (4−x)(4x+6)

and voila, that's the factored expression!

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