How do you factor $x^2 - 12x + 34$ ?

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Answer 1 · 2016-08-30T17:59:17

$x^2-12x+34=(x-6-sqrt(2))(x-6+sqrt(2))$

Complete the square then use the difference of squares identity:

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

with $a=(x-6)$ and $b=sqrt(2)$ as follows:

$x^2-12x+34$

$=x^2-12x+36-2$

$=(x-6)^2-(sqrt(2))^2$

$=((x-6)-sqrt(2))((x-6)+sqrt(2))$

$=(x-6-sqrt(2))(x-6+sqrt(2))$

How do you factor x^2 - 12x + 34x^2 - 12x + 34?