Factor the polynomial by grouping.
-$3 x ^ { 4 } - 8 x ^ { 2 } + 9 x ^ { 2 } - 24$
A) $\left( 3 x ^ { 2 } + 3 \right) \left( x ^ { 2 } - 8 \right)$
B) $\left( x ^ { 2 } + 3 \right) \left( 3 x ^ { 2 } - 8 \right)$
C)(x + 3)(8x - 3)
D)prime

Question

Quizplus · Accepted Answer

First, combine like terms: $3x^4 - 8x^2 + 9x^2 - 24 = 3x^4 + x^2 - 24$. Then, factor by grouping: $x^2(3x^2 + 1) - 24$, which doesn't directly lead to any of the given options. However, recognizing a mistake in the initial step (it should be $3x^4 + x^2 - 24$, correctly factored as $3x^4 - 24 + x^2$, still doesn't match the provided options directly. The correct approach is to initially group as $3x^4 - 8x^2 + 9x^2 - 24$, then factor each pair: $x^2(3x^2 - 8) + 3(3x^2 - 8)$, leading to $(x^2 + 3)(3x^2 - 8)$, which matches option B. My explanation mistakenly led to a reevaluation of the problem-solving process, but the correct answer based on the initial problem statement is B.

Factor the Polynomial by Grouping 3x4−8x2+9x2−243 x ^ { 4 } - 8 x ^ { 2 } + 9 x ^ { 2 } - 243x4−8x2+9x2−24

Factor the Polynomial by Grouping $3 x ^ { 4 } - 8 x ^ { 2 } + 9 x ^ { 2 } - 24$