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What is the expression in factored form?

2x2+16x+24

1 answer

To find the expression in factored form, we need to first factor out the greatest common factor, if possible.

In this case, the greatest common factor of the terms 2x^2, 16x, and 24 is 2. Therefore, we can factor out a 2 from each term:

2(x^2 + 8x + 12)

Next, we need to factorize the quadratic trinomial inside the parentheses. We are looking for two binomials that multiply together to give us the trinomial.

The factors of the first term x^2 are x and x.
The factors of the last term 12 are 1 and 12, or 2 and 6, or 3 and 4.

Considering the middle term, the product of the outer and inner terms should sum up to 8x. We can find suitable factors by trying different combinations:

(x + 2)(x + 6)

Now we have factored the quadratic trinomial (x^2 + 8x + 12) as (x + 2)(x + 6). Therefore, the expression in factored form is:

2(x + 2)(x + 6)