Factor by grouping. -8x² + 6xt - 9t² A) ( 8x - 3t)(x + 3t) B) ( 4x + 3t)( 2x - 3t) C) ( 4x - 3t)( 2x + 3t) D) Prime

Question

Quizplus · Accepted Answer

The expression can be rewritten as $8x^3 + 6x - 9t^3$. Factoring by grouping, we first factor out the greatest common factor (GCF) from each group: $2x(4x^2 + 3) - 3t(3t^2 + 3)$. Recognizing the sum and difference of cubes, we get $(2x - 3t)(4x^2 + 3t^2 + 6)$. However, the correct factorization aligns with the pattern for factoring a sum and difference of cubes, leading to the choice (C) $(4x - 3t)(2x + 3t)$, which correctly represents the factorization of the original expression.

Factor by Grouping. -8x2 + 6xt - 9t2

Factor by Grouping. -8x² + 6xt - 9t²