You have several boxes with the same dimensions. they have a combined volume of 4x4 - 21x3 - 46x2 + 219x + 180. determine whether the binomial below could represent the number of boxes you have.

Question

Mathematics

Eva Cooley

10 January, 08:31

You have several boxes with the same dimensions. they have a combined volume of 4x4 - 21x3 - 46x2 + 219x + 180. determine whether the binomial below could represent the number of boxes you have.

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Answers (1)

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Ariel Newman · Answer 1

The following are the choices for this problem:A. x+4 B. x+3 C. x-5 D. 4x+3

Factoring 4x^4-21x^3-46x^2+219x+180, this will give us then the short answer of x+4.

The factor theorem states that if x-n is a factor of function f (x) = 4x^4-21^3-46^2+219x+180 then f (x) = 0.

So let us evaluate f (-4) which gives 4 (256) - 21 (-64) - 46 (16) + 219 (-4) + 180 = 936

Since the function f (-4) does not equate to zero, we could say that x + 4 is not a factor.

So using x+3: f (-3) = 4 (81) - 21 (-27) - 46 (9) + 219 (-3) + 180 = 0, so x+3 is a factor.