the volume of a rectangular prism is given by the expression 10x³ + 46x² - 21x - 27. the area of the base of…

the volume of a rectangular prism is given by the expression 10x³ + 46x² - 21x - 27. the area of the base of the prism is given by the expression 2x² + 8x - 9. which of the following expressions represents the height of the prism? (v = bh)\n8x - 3\n3x - 5\n5x + 3\n42x + 3\ndone

the volume of a rectangular prism is given by the expression 10x³ + 46x² - 21x - 27. the area of the base of the prism is given by the expression 2x² + 8x - 9. which of the following expressions represents the height of the prism? (v = bh)\n8x - 3\n3x - 5\n5x + 3\n42x + 3\ndone

Answer

Explanation:

Step1: Recall the volume formula

Given $V = Bh$, we can find the height $h=\frac{V}{B}$. Here, $V = 10x^{3}+46x^{2}-21x - 27$ and $B=2x^{2}+8x - 9$.

Step2: Perform polynomial long - division

Divide $10x^{3}+46x^{2}-21x - 27$ by $2x^{2}+8x - 9$. [ \begin{align*} \frac{10x^{3}+46x^{2}-21x - 27}{2x^{2}+8x - 9}&=\frac{10x^{3}+40x^{2}-45x+6x^{2}+24x - 27}{2x^{2}+8x - 9}\ &=\frac{5x(2x^{2}+8x - 9)+3(2x^{2}+8x - 9)}{2x^{2}+8x - 9}\ &=5x + 3 \end{align*} ]

Answer:

C. $5x + 3$