Factor the following trinomial completely. $x ^ { 2 } + 4 x y - 12 y ^ { 2 }$
A) ( x + 2 y )( x + 6 y )
B) ( x + 2 y )( x $-$ 6 y )
C) ( x $-$ 2 y )( x $-$ 6 y )
D) x ( x + 4 y ) $-$ 12 y
E) ( x $-$ 2 y )( x + 6 y )

Question

Quizplus · Accepted Answer

To factor the trinomial $x^2 + 4xy - 12y^2$, we look for two numbers that multiply to $ac$ (where $a = 1$ for $x^2$ and $c = -12y^2$, so $ac = -12y^2$) and add to $b$ (where $b = 4y$). The numbers -2y and +6y work because $(-2y) \cdot (6y) = -12y^2$ and $(-2y) + (6y) = 4y$. Thus, the trinomial factors as $(x - 2y)(x + 6y)$.

Factor the Following Trinomial Completely x2+4xy−12y2x ^ { 2 } + 4 x y - 12 y ^ { 2 }x2+4xy−12y2

Factor the Following Trinomial Completely $x ^ { 2 } + 4 x y - 12 y ^ { 2 }$