Factor the polynomial completely. If the polynomial cannot be factored, write "prime."
-$x y ^ { 2 } + 2 y ^ { 2 } - 9 x - 18$
A) $( x - 2 ) ( y + 3 ) ( y - 3 )$
B) $( x + 2 ) ( y - 3 ) ^ { 2 }$
C) $( x + 2 ) \left( y ^ { 2 } - 9 \right)$
D) $( x + 2 ) ( y + 3 ) ( y - 3 )$

Question

Quizplus · Accepted Answer

First, group terms: $xy^2 - 9x + 2y^2 - 18$. Factoring by grouping, we get $x(y^2 - 9) + 2(y^2 - 9)$, which simplifies to $(x + 2)(y^2 - 9)$. Since $y^2 - 9$ is a difference of squares, it factors further into $(y + 3)(y - 3)$, resulting in the final factorization $(x + 2)(y + 3)(y - 3)$.

Factor the Polynomial Completely xy2+2y2−9x−18x y ^ { 2 } + 2 y ^ { 2 } - 9 x - 18xy2+2y2−9x−18

Factor the Polynomial Completely $x y ^ { 2 } + 2 y ^ { 2 } - 9 x - 18$