Respuesta :

mhanifa

Answer:

(2x - 1)

Step-by-step 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

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