Use synthetic division to find the quotient and remainder.
-$$\left( 2 x ^ { 4 } - x ^ { 3 } - 15 x ^ { 2 } + 3 x \right) \div ( x + 3 )$$
A) $2 x ^ { 3 } + 5 x ^ { 2 } + 3 + \frac { 9 } { x + 3 }$
B) $2 x ^ { 3 } - 7 x ^ { 2 } + 6 x - 15 - \frac { 45 } { x + 3 }$
C) $2 x ^ { 3 } - 7 x ^ { 2 } + 6 x - 15 + \frac { 45 } { x + 3 }$
D) $2 x ^ { 3 } - 5 x ^ { 2 } + 3 - \frac { 9 } { x + 3 }$

Question

Quizplus · Accepted Answer

To use synthetic division for dividing by $x + 3$, we use $-3$ as the divisor. The coefficients of the polynomial are 2, -1, -15, 3, and 0 (since there's no constant term). The synthetic division process yields a quotient of $2x^3 - 7x^2 + 6x - 15$ and a remainder of 45, making the correct answer $2x^3 - 7x^2 + 6x - 15 + \frac{45}{x + 3}$.

Use Synthetic Division to Find the Quotient and Remainder (2x4−x3−15x2+3x)÷(x+3)\left( 2 x ^ { 4 } - x ^ { 3 } - 15 x ^ { 2 } + 3 x \right) \div ( x + 3 )(2x4−x3−15x2+3x)÷(x+3)

Use Synthetic Division to Find the Quotient and Remainder $\left( 2 x ^ { 4 } - x ^ { 3 } - 15 x ^ { 2 } + 3 x \right) \div ( x + 3 )$