Factor. Assume that variables used as exponents represent positive integers.
-$$7 x ^ { 2 n } + 5 x ^ { n } - 18$$
A) $\left( \mathrm { x } ^ { \mathrm { n } } - 9 \right) \left( 7 \mathrm { x } ^ { \mathrm { n } } + 2 \right)$
B) $\left( x ^ { n } + 2 \right) \left( 7 x ^ { n } - 9 \right)$
C) $\left( x ^ { n } - 2 \right) \left( 7 x ^ { n } + 9 \right)$
D) prime polynomial

Question

Quizplus · Accepted Answer

To factor the given polynomial $7x^{2n} + 5x^n - 18$, we look for two numbers that multiply to $7(-18) = -126$ and add to $5$. These numbers are $14$ and $-9$. Thus, we can rewrite the middle term and factor by grouping: $7x^{2n} - 9x^n + 14x^n - 18$, which leads to $(x^n + 2)(7x^n - 9)$.

Factor Assume That Variables Used as Exponents Represent Positive Integers 7x2n+5xn−187 x ^ { 2 n } + 5 x ^ { n } - 187x2n+5xn−18

Factor Assume That Variables Used as Exponents Represent Positive Integers $7 x ^ { 2 n } + 5 x ^ { n } - 18$