Divide using long division.
-$$\left( 5 x ^ { 4 } - 38 x ^ { 3 } + 22 x ^ { 2 } - 11 x + 28 \right) \div ( 7 - x )$$
A) $- 5 x ^ { 3 } + 3 x ^ { 2 } - x + 4$
B) $- 5 x ^ { 3 } + 3 x ^ { 2 } - x - 4$
C) $- 5 x ^ { 3 } + 3 x ^ { 2 } - x - 4 + \frac { 56 } { 7 }$
D) $- 5 x ^ { 3 } + 3 x ^ { 2 } + x - 4$

Question

Quizplus · Accepted Answer

To divide $(5x^4 - 38x^3 + 22x^2 - 11x + 28)$ by $(7 - x)$, we rewrite the divisor as $(-x + 7)$ for easier division. The first term of the quotient is obtained by dividing $5x^4$ by $-x$, which gives $-5x^3$. Multiplying $(-x + 7)$ by $-5x^3$ and subtracting from the dividend, we continue this process iteratively. The correct quotient, without remainder, is $-5x^3 + 3x^2 - x + 4$, matching option A.

Divide Using Long Division (5x4−38x3+22x2−11x+28)÷(7−x)\left( 5 x ^ { 4 } - 38 x ^ { 3 } + 22 x ^ { 2 } - 11 x + 28 \right) \div ( 7 - x )(5x4−38x3+22x2−11x+28)÷(7−x)

Divide Using Long Division $\left( 5 x ^ { 4 } - 38 x ^ { 3 } + 22 x ^ { 2 } - 11 x + 28 \right) \div ( 7 - x )$