Chapter 6, Problem 7MCQ

To determine

To Calculate: The polynomial expression represents the base of rectangular prism with volume $6x^3+19x^2+2x-3$ and height $x+3$ where $x\ne 0$ .Given options are

  $\begin{array}{l}A.6x^4+37x^3+59x^2+3x-9\\ B.6x^2+x+1\\ C.6x^2+x-1\\ D.6x+1\end{array}$

Answer to Problem 7MCQ

The correct option is $C$.

Explanation of Solution

Given information:

The volume of rectangular prism is $6x^3+19x^2+2x-3$ and height $x+3$ where $x\ne 0$ .

Formula used:

The volume of rectangular prism is base multiply by height.

Calculation:

Consider the volume of rectangular prism is $6x^3+19x^2+2x-3$ and height $x+3$ where $x\ne 0$ .

Recall that the volume of rectangular prism is base multiply by height.

Now check each of the option which satisfies the condition.

For option A:

Volume is $6x^3+19x^2+2x-3$ , height is $x+3$ and base is $6x^4+37x^3+59x^2+3x-9$ .

  Base $\times$ height $=$ $\left(6x^4+37x^3+59x^2+3x-9\right)$ $\times$ $\left(x+3\right)$

  $\left(6x^4+37x^3+59x^2+3x-9\right)x+\left(6x^4+37x^3+59x^2+3x-9\right)\times 3=6x^5+55x^4+170x^3+62x^2-18$

This is not equal to given volume.

Therefore option A is not correct answer.

For option B:

Volume is $6x^3+19x^2+2x-3$ , height is $x+3$ and base is $6x^2+x+1$ .

  Base $\times$ height $=$ $\left(6x^2+x+1\right)$ $\times$ $\left(x+3\right)$

  $\left(6x^2+x+1\right)x+\left(6x^2+x+1\right)\times 3=6x^3+19x^2+4x+3$

This is not equal to given volume.

Therefore option B is not correct answer.

For option C:

Volume is $6x^3+19x^2+2x-3$ , height is $x+3$ and base is $6x^2+x-1$ .

  Base $\times$ height $=$ $\left(6x^2+x-1\right)$ $\times$ $\left(x+3\right)$

  $\left(6x^2+x-1\right)x+\left(6x^2+x-1\right)\times 3=6x^3+19x^2-2x-3$

This is equal to given volume.

Therefore option C is correct answer.

For option D:

Volume is $6x^3+19x^2+2x-3$ , height is $x+3$ and base is $6x+1$ .

  Base $\times$ height $=$ $6x+1$ $\times$ $\left(x+3\right)$

  $\left(6x+1\right)x+\left(6x+1\right)\times 3=6x^2+19x+3$

This is equal not to given volume.

Therefore option D is not correct answer.

Thus, the polynomial expression for base of rectangular prism is $6x^2+x-1$ .