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

1 Answer
Dec 22, 2015

Answer:

#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#