Divide using synthetic division.
-$$\left( 3 x ^ { 5 } + 6 x ^ { 4 } - 4 x ^ { 3 } + x ^ { 2 } - x + 130 \right) \div ( x + 3 )$$
A) $3 x ^ { 4 } - 3 x ^ { 3 } + 5 x ^ { 2 } + 14 x + 41 + \frac { 7 } { x + 3 }$
B) $3 x ^ { 4 } - 3 x ^ { 3 } + 5 x ^ { 2 } - 14 x - 42 + \frac { 7 } { x + 3 }$
C) $3 x ^ { 4 } - 3 x ^ { 3 } + 5 x ^ { 2 } - 15 x + 42 + \frac { 12 } { x + 3 }$
D) $3 x ^ { 4 } - 3 x ^ { 3 } + 5 x ^ { 2 } - 15 x - 42 + \frac { 12 } { x + 3 }$

Question

Quizplus · Accepted Answer

To perform synthetic division with $x + 3$, we use $-3$ as the divisor. The coefficients of the polynomial are brought down: $3, 6, -4, 1, -1, 130$. The synthetic division process yields the quotient $3x^4 - 3x^3 + 5x^2 + 14x + 41$ and a remainder of $7$, which gives the correct answer as $3 x ^ { 4 } - 3 x ^ { 3 } + 5 x ^ { 2 } + 14 x + 41 + \frac { 7 } { x + 3 }$.

Divide Using Synthetic Division (3x5+6x4−4x3+x2−x+130)÷(x+3)\left( 3 x ^ { 5 } + 6 x ^ { 4 } - 4 x ^ { 3 } + x ^ { 2 } - x + 130 \right) \div ( x + 3 )(3x5+6x4−4x3+x2−x+130)÷(x+3)

Divide Using Synthetic Division $\left( 3 x ^ { 5 } + 6 x ^ { 4 } - 4 x ^ { 3 } + x ^ { 2 } - x + 130 \right) \div ( x + 3 )$