the volume of a rectangular prism is $2x^{3}+9x^{2}-8x - 36$ with height $x + 2$. using synthetic division…

the volume of a rectangular prism is $2x^{3}+9x^{2}-8x - 36$ with height $x + 2$. using synthetic division, what is the area of the base?\n$2x^{3}+13x^{2}+18x$\n$2x^{3}+5x^{2}-18x$\n$2x^{2}+13x + 18$\n$2x^{2}+5x - 18$

the volume of a rectangular prism is $2x^{3}+9x^{2}-8x - 36$ with height $x + 2$. using synthetic division, what is the area of the base?\n$2x^{3}+13x^{2}+18x$\n$2x^{3}+5x^{2}-18x$\n$2x^{2}+13x + 18$\n$2x^{2}+5x - 18$

Answer

Explanation:

Step1: Set up synthetic division

For dividing $2x^{3}+9x^{2}-8x - 36$ by $x + 2$, use - 2 in synthetic division. Coefficients are 2, 9, - 8, - 36.

Step2: Bring down the first coefficient

Bring down 2.

Step3: Multiply and add

Multiply - 2 by 2 to get - 4, add to 9 gives 5. Then multiply - 2 by 5 to get - 10, add to - 8 gives - 18. Multiply - 2 by - 18 to get 36, add to - 36 gives 0.

Step4: Write the quotient

The quotient is $2x^{2}+5x - 18$. Since volume of prism $V=Bh$ (where $B$ is base - area and $h$ is height), and we divided volume by height, the quotient is the base - area.

Answer:

D. $2x^{2}+5x - 18$