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

1 Answer
Ratnaker Mehta
Jul 12, 2016

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

Explanation:

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).#

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