1
$\begingroup$

If $$x^2 + (c-2)x -c^2 -3c + 5$$ is divided by $x + c$, the remainder is $-1$. find the value of c

I replaced all the x value to -c and set it to an equation which equated to $-1$

I am confused what to do after that, show me the steps how I can retrieve the value of $c$

$\endgroup$
1
  • $\begingroup$ If you perform the substitution $x\mapsto c$ you can't get more than a quadratic in $c.$ What's confusing about that? Don't you know how to solve quadratic equations? $\endgroup$ – Allawonder Oct 20 '19 at 15:03
0
$\begingroup$

Given that: $$\begin{align}x^2 + (c-2)x -c^2 -3c + 5 & = (-c)^2 + (c-2)(-c) -c^2 -3c + 5 \\ & = c^2 - c^2 +2c -c^2 -3c + 5 \\ c^2 +c -5& = 1 \\ c^2 +c-6 &= 0 \\ (c+3)(c-2) & = 0 \implies \color {blue}{ \boxed {\text { c = 2 , -3}} }\end{align} $$

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.