How do you factor the trinomial $x^2 + 2x - 24$ ?

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Answer 1 · 2016-07-12T09:58:15

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

Let $P(x)=x^2+2x-24.$

Note that product of leading co-eff. and const. term $=1xx(-24)= -24,$ a negative no.

So, we have to find two factors of this product 24, such that their difference is $2$ =middle term coeff.

We find that, $6xx4=24, and, 6-4=2$

Accordingly, we split the middle term $2x$ as $6x-4x$ . Hence,

$P(x)= x^2+2x-24 =x^2+6x-4x-24 =x(x+6)-4(x+6)=(x+6)(x-4).$

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