How do you factor x² - 14x + 9?

1 Answer
May 13, 2016

x^2-14x+9=(x-7-2sqrt(10))(x-7+2sqrt(10))

Explanation:

One way is to complete the square and use the difference of squares identity:

a^2-b^2=(a-b)(a+b)

with a=(x-7) and b=2sqrt(10) as follows:

x^2-14x+9

=(x-7)^2-7^2+9

=(x-7)^2-40

=(x-7)^2-2^2*10

=(x-7)^2-(2sqrt(10))^2

=((x-7)-2sqrt(10))((x-7)+2sqrt(10))

=(x-7-2sqrt(10))(x-7+2sqrt(10))