# SMO 2015 Q10 Round 1

When a polynomial $f(x)$ is divided by $(x - 1)$and $(x + 5)$, the remainders are -6 and 6 respectively. Let $r(x)$ be the remainder when $f(x)$ is divided by $x^2 +4x - 5$. Find the value of $r(-2)$.

(A) 0 (B) 1 (c) 2 (D) 3 (E) 5

How does one do this sort of question?

I'm not experienced with polynomials, so it may seem a simple question to you but not to me. But please help! I'm a learner too :) Note by Timothy Wan
4 years, 8 months ago

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What is $r$ in $x^2+4r-5$?

- 4 years, 8 months ago

It's an error. Just corrected the note. Sorry!

- 4 years, 8 months ago

Have you read the remainder factor theorem? If so, how do you think this could apply?

Staff - 4 years, 8 months ago

yeah you are right, but here, we would apply more of Euclids Division Algorithm for polynomials. Won't we? (Which essentially constitutes the proof of remainder theorem)

- 4 years, 8 months ago

There are many equivalent ways of expressing the ideas involved in this question. I was pointing out one possible approach, which I think should be thought of given the phrasing of the question.

Staff - 4 years, 8 months ago

Since the divisor is of degree 2, $r(x)$ is linear and in the form $Ax+B$.

$f(1)=A(1)+B=A+B=-6$.

Also $f(-5)=A(-5)+B=-5A+B=6$.

Solving the simultaneous equations, $A=-2,B=-4$

$r(x)=-2x-4$

$\therefore r(-2)=-2(-2)-4=0$

Is this a correct solution?

- 4 years, 8 months ago

You got confused between $f(x)$ and $r(x)$.

- 4 years, 8 months ago