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

1 Answer
Dec 22, 2015

y = (x - 5)(x - 2)

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 (x + n_1)(x + n_2), which will represent the factored form of y.

y = (x + n_1)(x + n_2)

where n_1 and n_2 are the numbers we just found.

Thus, we get

y = (x - 5)(x - 2)

To confirm this, apply FOIL.

y = x^2 - 5x - 2x + 10

which reduces to

y = x^2 - 7x + 10