Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime.
-$14 x ^ { 2 } - 49 x - 28$
A) $7 ( 2 x + 1 ) ( x - 4 )$
B) prime
C) $( 14 x - 7 ) ( x + 4 )$
D) $7 ( 2 x - 1 ) ( x + 4 )$

Question

Quizplus · Accepted Answer

The polynomial $14x^2 - 49x - 28$ can be factored by first finding two numbers that multiply to $14 \times -28 = -392$ and add to $-49$. These numbers are $-56$ and $8$. Rewriting the middle term and factoring by grouping gives: $14x^2 - 56x + 8x - 28 = 14x(x - 4) + 8(x - 4) = (14x + 8)(x - 4) = 7(2x + 1)(x - 4)$.

Factor Completely Using the Grouping Method to Factor Trinomials 14x2−49x−2814 x ^ { 2 } - 49 x - 2814x2−49x−28

Factor Completely Using the Grouping Method to Factor Trinomials $14 x ^ { 2 } - 49 x - 28$