Question

The volume of the rectangular prism is 60x3 + 145x2 + 70x. Factor to find the possible expressions for length, width and height of the prism.

Answer 1

The probable expressions for length, width, and height would be:

5x

3x + 2

4x + 7

Step-by-step explanation:

Given that,

Volume of the rectangular prism = $60x^{3} + 145x^2 + 70x$

As we know,

Volume of the rectangular prism = Length × Width × Height

A.T.Q.

Using factorization for the given equation,

Volume = $60x^{3} + 145x^2 + 70x$

by taking 5x as common, we get

= $5x(12x^2 + 29x + 14)$

= $5x(12x^2 + 21x + 8x + 14)$

Now,

= $5x(3x(4x + 7) + 2(4x + 7)$

= $5x[(3x + 2) (4x + 7)]$

= $5x (3x + 2) (4x + 7)$

Thus, the probable expressions for length, width, and height would be:

5x, (3x + 2), and (4x + 7).

Learn more: Rectangular Prism

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