Factor the polynomial completely. If the polynomial cannot be factored, write "prime."
-$x ^ { 2 } + 5 x y - 14 y ^ { 2 }$
A) $( x - 7 y ) ( x + y )$
B) prime
C) $( x + 7 y ) ( x - 2 y )$
D) $( x - 7 y ) ( x + 2 y )$

Question

Quizplus · Accepted Answer

The polynomial $x^2 + 5xy - 14y^2$ can be factored by looking for two numbers that multiply to $ac$ (where $a$ is the coefficient of $x^2$ and $c$ is the constant term, in this case, $-14y^2$) and add to $b$ (the coefficient of the middle term, in this case, $5y$). The numbers 7 and -2 fit this criterion because $7 \times -2 = -14$ and $7 + (-2) = 5$. Therefore, the polynomial factors into $(x + 7y)(x - 2y)$.

Factor the Polynomial Completely x2+5xy−14y2x ^ { 2 } + 5 x y - 14 y ^ { 2 }x2+5xy−14y2

Factor the Polynomial Completely $x ^ { 2 } + 5 x y - 14 y ^ { 2 }$