Factor using the ac-method.
-$21 x ^ { 2 } - 91 x - 70$
A) $( 21 x + 14 ) ( x - 5 )$
B) prime
C) $7 ( 3 x + 2 ) ( x - 5 )$
D) $7 ( 3 x - 2 ) ( x + 5 )$

Question

Quizplus · Accepted Answer

The ac-method involves multiplying the coefficient of $x^2$ (which is 21) by the constant term (-70), giving -1470. We look for two numbers that multiply to -1470 and add to the coefficient of $x$ (-91). Those numbers are -105 and 14. Factoring by grouping with these numbers, we can rewrite the equation as $21x^2 - 105x + 14x - 70$, which simplifies to $7(3x + 2)(x - 5)$.

Factor Using the Ac-Method 21x2−91x−7021 x ^ { 2 } - 91 x - 7021x2−91x−70

Factor Using the Ac-Method $21 x ^ { 2 } - 91 x - 70$