Factor the polynomial by substitution.
-$$8 x ^ { 4 } + 18 x ^ { 2 } + 9$$
A) $\left( 4 x ^ { 2 } + 3 \right) \left( 2 x ^ { 2 } + 3 \right)$
B) $\left( 8 x ^ { 2 } + 3 \right) \left( x ^ { 2 } + 3 \right)$
C) $\left( 4 x ^ { 2 } - 3 \right) \left( 2 x ^ { 2 } - 3 \right)$
D) $\left( 4 x ^ { 2 } + 1 \right) \left( 2 x ^ { 2 } + 9 \right)$

Question

Quizplus · Accepted Answer

Let $u = x^2$, then the polynomial becomes $8u^2 + 18u + 9$. Factoring this quadratic gives $(4u + 3)(2u + 3)$. Substituting back $u = x^2$ gives $(4x^2 + 3)(2x^2 + 3)$.

Factor the Polynomial by Substitution 8x4+18x2+98 x ^ { 4 } + 18 x ^ { 2 } + 98x4+18x2+9

Factor the Polynomial by Substitution $8 x ^ { 4 } + 18 x ^ { 2 } + 9$