Factor the polynomial completely. $p ( x ) = x ^ { 6 } - 6 x ^ { 4 } + 9 x ^ { 2 }$
A) $x ^ { 4 } ( x - \sqrt { 3 } ) ^ { 2 }$
B) $x ^ { 2 } ( x - 3 ) ^ { 2 } ( x + 3 ) ^ { 2 }$
C) $x ^ { 2 } \left( x ^ { 4 } - 6 x ^ { 2 } - 9 \right)$
D) $x ^ { 4 } ( x + 9 ) ^ { 2 }$
E) none

Question

Quizplus · Accepted Answer

The polynomial $p(x) = x^6 - 6x^4 + 9x^2$ can be factored as $x^2(x^4 - 6x^2 + 9)$. Recognizing the trinomial as a perfect square, it further factors to $x^2(x^2 - 3)^2$, which is not listed among the options provided.

Factor the Polynomial Completely p(x)=x6−6x4+9x2p ( x ) = x ^ { 6 } - 6 x ^ { 4 } + 9 x ^ { 2 }p(x)=x6−6x4+9x2

Factor the Polynomial Completely $p ( x ) = x ^ { 6 } - 6 x ^ { 4 } + 9 x ^ { 2 }$