Question

Factor$x^2-7xy-10y^2$

Short answer

The factored form is$(x-5y)(x-2y)$

Step-by-step solution

Given information

Given the polynomial$x^2-7xy-10y^2$

Create the factor table

The table is

Factors of$-10$	Sum of factors
$1,-12$	$1-12=-11$
$2,-6$	$2-6=-4$
$-2,-5$	$-2-5=-7$

Use m,n as last terms of factors and form the factored polynomial

Here,

$$\begin{gathered} m,n=-2,-5 \\ m+n=-7 \\ m\times n=10 \end{gathered}$$

Substitute the values to form the factored form

The factored form is$(x-5y)(x-2y)$