# How to factorize a quadratic expression with an extra constant?

Pretty simple question that I never thought id get stuck on. How do I factor $x^2 - 6x + 8 - d$ into a form $(x - a)(x - b)$ where $d$ is just an unknown constant ? Been looking online but it seems all the tutorials / videos but have not found anything useful.

EDIT: Im silly for not remembering the formula $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

• Hint: use the quadratic formula. – lulu Apr 18 '18 at 20:23
• Doh ! Im an idiot for not remembering that.. Thanks... – Kong Apr 18 '18 at 20:24
• Note that the $c$ in the quadradic formula is $c = 8-d$ in your expression. That is, $a=1, b= -6, c=8-d$. – amWhy Apr 18 '18 at 20:29

$x^2 + x(a + b) + ab = (x + a)(x + b)$
$x^2 - 6x + 8 - c = (x + a)(x + b)$ , where
$ab = 8 - c$
$a + b = -6$