Perform the division.
-$\left(x^{4}-625\right) \div(x+5)$
A) $x^{3}-5 x^{2}+25 x-125$
B) $x^{2}+5 x+25$
C) $x^{3}+5 x^{2}-25 x+125$
D) $x^{3}+5 x^{2}+25 x+125$

Question

Quizplus · Accepted Answer

The given expression $\left(x^{4}-625\right) \div(x+5)$ can be simplified by recognizing that $x^4 - 625$ is a difference of squares, where $x^4 = (x^2)^2$ and $625 = 25^2$. Thus, $x^4 - 625 = (x^2 - 25)(x^2 + 25)$. Further simplifying, $x^2 - 25$ can also be factored as a difference of squares, yielding $(x - 5)(x + 5)$. However, since we are dividing by $x + 5$, we only need to consider the quotient when $x^4 - 625$ is divided by $x + 5$, which simplifies directly to $x^3 - 5x^2 + 25x - 125$, without needing to explicitly factor the expression as described. This is a standard result from polynomial long division or synthetic division.

Perform the Division (x4−625)÷(x+5)\left(x^{4}-625\right) \div(x+5)(x4−625)÷(x+5) A) x3−5x2+25x−125x^{3}-5 x^{2}+25 x-125x3−5x2+25x−125 B) x2+5x+25x^{2}+5 x+25x2+5x+25 C) x3+5x2−25x+125x^{3}+5 x^{2}-25 x+125x3+5x2−25x+125

Perform the Division $\left(x^{4}-625\right) \div(x+5)$ A) $x^{3}-5 x^{2}+25 x-125$ B) $x^{2}+5 x+25$ C) $x^{3}+5 x^{2}-25 x+125$