How do you factor the expression $-4x^2 + 10x + 24$ ?

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Answer 1 · 2015-12-30T19:33:05

$(4-x)(4x+6)$

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 $x^2$ 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:

$-4x^2 + (16-6)x + 24$
$-4x^2 + 16x - 6x + 24$

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!

How do you factor the expression -4x^2 + 10x + 24-4x^2 + 10x + 24?