Fully factor the given trinomial. Do not include spaces in your answer. 24x^2+56x+32

Question

would be best to get the awnser very quick

Answer 1

24x² + 56x + 32

We need to start by factoring out the largest number we can, so what is the largest common factor of 24, 56, and 32? The answer to that is 8.

8[3x² + 7x + 4]

What are the factors of the 3rd term (4)?

1, 2, 4

8[(3x + ?)(x + ?)

Now, the factors that we mltply to come up with the +4 will also be added togrether to come up with the 7 (coefficient ofthe 2nd term). The trick to factoring a polynomial like this one is that the leading coefficient (coefficient of the 1st term) is NOT 1 so one of 4 will be multiplied by 3 before we add it to the oher factor to get a total of 7.

If we use the factors of 2 × 2 to get 4, then one of the 2s will be multiplied by 3, giving us 2(3) + 2 = 8, NOT 7, so let's try the factors of 4 and 1. We know that if we were to multiply the 4 by 3, we would get 12 + 1 which doesn't work, but if we multiply the 1 by 3 we get 4 + 1(3) = 7. That works!

So, here we go. When we factor the given polynomial, we get:

8[(3x + 4)(x + 1)]

Let's multiply it back out to make sure it's right.

8[3x(x + 1) + 4(x + 1)]

8[3x² + 3x + 4x + 4]

8[3x² + 7x + 4]

24x² + 56x + 32

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Answer 2

24x^2 + 56x + 32 divide by 8

= 8(3x^2 + 7x + 4)

= 8(x+1)(3x+4)

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