Factor by grouping. -12x² + 7xt - 12t² A) ( 4x + 3t)( 3x - 4t) B) ( 12x - 3t)(x + 4t) C) ( 4x - 3t)( 3x + 4t) D) Prime

Question

Quizplus · Accepted Answer

The expression can be rewritten as $12x^2 + 7xt - 12t^2$. Factoring by grouping, we first look for factors of $12x^2$ and $-12t^2$ that when multiplied give a product of $12x^2(-12t^2) = -144x^2t^2$ and when added give the middle term $7xt$. The factors $16xt$ and $-9xt$ work since $16xt - 9xt = 7xt$. So, we rewrite the middle term $7xt$ as $16xt - 9xt$, giving us $12x^2 + 16xt - 9xt - 12t^2$. Grouping the terms, we get $4x(3x + 4t) - 3t(3x + 4t)$, which factors to $(4x - 3t)(3x + 4t)$.

Factor by Grouping. -12x2 + 7xt - 12t2

Factor by Grouping. -12x² + 7xt - 12t²