Factor. Assume that variables used as exponents represent positive integers.
-$$25 x ^ { 2 n } - 60 x ^ { n } + 36$$
A) $\left( 5 x ^ { n } - 6 \right) ^ { 2 }$
B) $\left( 25 \mathrm { x } ^ { \mathrm { n } } + 1 \right) \left( \mathrm { x } ^ { \mathrm { n } } + 36 \right)$
C) $\left( 5 x ^ { n } - 6 \right) \left( 5 x ^ { n } + 6 \right)$
D) $\left( 5 x ^ { n } + 6 \right) ^ { 2 }$

Question

Quizplus · Accepted Answer

The given expression is a perfect square trinomial, factoring into $(5x^n - 6)^2$, since $25x^{2n}$ is the square of $5x^n$, $36$ is the square of $6$, and $2 \cdot 5x^n \cdot 6 = 60x^n$, which matches the middle term.

Factor Assume That Variables Used as Exponents Represent Positive Integers 25x2n−60xn+3625 x ^ { 2 n } - 60 x ^ { n } + 3625x2n−60xn+36

Factor Assume That Variables Used as Exponents Represent Positive Integers $25 x ^ { 2 n } - 60 x ^ { n } + 36$