Divide.
-$$\left( 5 x ^ { 4 } - 7 x ^ { 2 } + 35 x ^ { 3 } - 49 x \right) \div ( 5 x + 35 )$$
A) $x ^ { 3 } - \frac { 7 } { 5 } x - \frac { 98 x } { 5 x + 35 }$
B) $x ^ { 3 } - 35 x + \frac { 25 x } { 5 x + 35 }$
C) $x ^ { 3 } + \frac { 7 } { 5 } x$
D) $x ^ { 3 } - \frac { 7 } { 5 } x$

Question

Quizplus · Accepted Answer

First, factor out the common factor in the divisor, $5x + 35 = 5(x + 7)$. Then, divide each term in the dividend by $5(x + 7)$. Notice that $35x^3$ and $-49x$ can be rewritten as $5x^3 \cdot 7$ and $-7 \cdot 5x$, making them divisible by $5(x + 7)$. After simplification, the terms $5x^4$ and $-7x^2$ yield $x^3$ and $-\frac{7}{5}x$, respectively, with no remainder.

Divide - (5x4−7x2+35x3−49x)÷(5x+35)\left( 5 x ^ { 4 } - 7 x ^ { 2 } + 35 x ^ { 3 } - 49 x \right) \div ( 5 x + 35 )(5x4−7x2+35x3−49x)÷(5x+35)

Divide
- $\left( 5 x ^ { 4 } - 7 x ^ { 2 } + 35 x ^ { 3 } - 49 x \right) \div ( 5 x + 35 )$