# How do you factor y= x^2 - 7x + 10 ?

Dec 22, 2015

$y = \left(x - 5\right) \left(x - 2\right)$

#### Explanation:

Our goal is to think of two numbers that multiply to give $10$ but add to $- 7$.

One pair of number sounds particularly good; $- 5$ and $- 2$. Add them together, and you'll get $- 7$. Multiply them, you get $10$.

For a simple quadratic like this one we can insert these numbers into an expression of the form $\left(x + {n}_{1}\right) \left(x + {n}_{2}\right)$, which will represent the factored form of $y$.

$y = \left(x + {n}_{1}\right) \left(x + {n}_{2}\right)$

where ${n}_{1}$ and ${n}_{2}$ are the numbers we just found.

Thus, we get

$y = \left(x - 5\right) \left(x - 2\right)$

To confirm this, apply FOIL.

$y = {x}^{2} - 5 x - 2 x + 10$

which reduces to

$y = {x}^{2} - 7 x + 10$