Question

URGENT HELP ASAP

The volume of a rectangular prism is expressed as 36x3+60x2 + x - 20. Its length is (3x + 4) and its width
is (6x + 5). What is the height of the prism?

Answer 1

(2x - 1)

Explanation:

• Volume of a rectangular prism is: V = lwh, where l= lenght, w= width, h= height

Given

• V = 36x³ + 60x² + x - 20
• l = (3x + 4)
• w = (6x + 5)

and

• h = ?

Solution

Since the volume is the polynomial of third degree and the two of the factors are of the first degree, the third factor is going to be a first degree as well in the format of (mx +n)

So we have below equation:

• 36x³ + 60x² + x - 20 = (3x + 4)(6x + 5) (mx + n)

We can work out the value of m and n:

• 3x*6x*mx = 36x³
• 18mx³ = 36 x³
• m = 2

And

• 4*5*n = -20
• 20n = -20
• n = -1

So we get the factor of (mx + n) = (2x - 1)

Therefore

• h = (2x - 1)

Proof of the polynimial is correct:

• (3x + 4)(6x +5)(2x - 1) =
• (18x²+39x+20)(2x - 1) =
• 36x³ - 18x² + 78x² - 39x + 40x - 20 =
• 36x² + 60x² + x - 20