Factorize completely x^2+x^2y+3x-10y+3xy-10

idontknow Dec 2015 1,084 169 Earth Mar 3, 2020 #2 solve x^2+x^2y+3x-10y+3xy-10=0 for x. then x^2+x^2y+3x-10y+3xy-10=(1+y)(x-x_1 )(x-x_2).

skipjack Forum Staff Dec 2006 21,481 2,470 Mar 3, 2020 #3 $\begin{align*}x^2 + x^2y + 3x - 10y + 3xy - 10 &= x^2 + x^2y + 3x + 3xy - 10y - 10 \\ &= x^2(1 + y) + 3x(1 + y) - 10(1 + y) \\ &= (x^2 + 3x - 10)(y + 1) \\ &= (x + 5)(x - 2)(y + 1)\end{align*}$ Reactions: topsquark

$\begin{align*}x^2 + x^2y + 3x - 10y + 3xy - 10 &= x^2 + x^2y + 3x + 3xy - 10y - 10 \\ &= x^2(1 + y) + 3x(1 + y) - 10(1 + y) \\ &= (x^2 + 3x - 10)(y + 1) \\ &= (x + 5)(x - 2)(y + 1)\end{align*}$