Question

You have several boxes with the same dimensions. They have a combined volume of 4X^4 - 21X^3 - 46X^2 + 219X + 180. Determine whether the binomials below could represent the number of boxes you have:

a) (2X^2 - 15X - 20)(2X^2 + 11X + 9)
b) (X^2 - 10X - 9)(4X^2 + 24X + 20)
c) (X^2 - 9X - 10)(4X^2 + 20X + 18)
d) (3X^2 - 19X - 18)(X^2 + 10X + 21)

Answer 1

Option D). The given expression can be factored into (2X - 9)(X - 4)(X + 5)(2X + 6). Among the given binomials, only (3X^2 - 19X - 18)(X^2 + 10X + 21) matches one of the factors, so it could represent the number of boxes.

Step-by-step explanation:

The given expression is the combined volume of several boxes. In order to determine if the binomials represent the number of boxes, we can factorize the expression and see if any of the binomials match with the factors.

Factoring the expression 4X^4 - 21X^3 - 46X^2 + 219X + 180, we get (2X - 9)(X - 4)(X + 5)(2X + 6).

Comparing this with the binomials:

a) (2X^2 - 15X - 20)(2X^2 + 11X + 9) - This does not match any of the factors.

b) (X^2 - 10X - 9)(4X^2 + 24X + 20) - This does not match any of the factors.

c) (X^2 - 9X - 10)(4X^2 + 20X + 18) - This does not match any of the factors.

d) (3X^2 - 19X - 18)(X^2 + 10X + 21) - This matches the factor (2X - 9)(X - 4), so it could represent the number of boxes.