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What is the expression in factored form?
2x2+16x+24
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)