Simplify the rational expression.
-$\frac { w ^ { 3 } - 5 w ^ { 2 } - 2 w + 10 } { w ^ { 2 } - 10 w + 25 }$
A) $\frac { w + 5 } { w ^ { 2 } + 2 }$
B) $\frac { w ^ { 2 } - 2 } { w - 5 }$
C) $\frac { w ^ { 2 } + 2 } { w + 5 }$
D) $\frac { w ^ { 2 } - 5 } { w - 2 }$

Question

Quizplus · Accepted Answer

To simplify the given expression, factor both the numerator and the denominator. The numerator $w^3 - 5w^2 - 2w + 10$ can be factored by grouping: $w^2(w - 5) - 2(w - 5)$, which simplifies to $(w^2 - 2)(w - 5)$. The denominator $w^2 - 10w + 25$ can be factored as $(w - 5)(w - 5)$ or $(w - 5)^2$. Thus, the simplified expression is $\frac{w^2 - 2}{w - 5}$.

Simplify the Rational Expression w3−5w2−2w+10w2−10w+25\frac { w ^ { 3 } - 5 w ^ { 2 } - 2 w + 10 } { w ^ { 2 } - 10 w + 25 }w2−10w+25w3−5w2−2w+10​

Simplify the Rational Expression $\frac { w ^ { 3 } - 5 w ^ { 2 } - 2 w + 10 } { w ^ { 2 } - 10 w + 25 }$