How do you factor the trinomial # x^2 - 4 x - 12#?

Answer 1

Kennedy Adams

#x^2-4x-12 = (x-6)(x+2)#

Find a pair of factors of #12# which differ by #4#.

The pair #6, 2# works, in that #6*2=12# and #6-2=0#

Hence:

#x^2-4x-12 = (x-6)(x+2)#

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Answer 2

Genesis Allen

To factor the trinomial (x^2 - 4x - 12), you can use the following steps:

Identify two numbers that multiply to the constant term (-12) and add up to the coefficient of the linear term (-4).
Rewrite the middle term using these two numbers.
Factor by grouping or use the factoring method based on the form of the trinomial.

For this trinomial:

(x^2 - 4x - 12)

The two numbers that multiply to -12 and add up to -4 are -6 and 2.

Rewrite the middle term:

(x^2 - 6x + 2x - 12)

Factor by grouping:

(x(x - 6) + 2(x - 6))

Now, factor out the common binomial factor:

((x + 2)(x - 6))

So, the factored form of the trinomial is ((x + 2)(x - 6)).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.