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 :)

## Comments

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TopNewestWhat is \(r\) in \(x^2+4r-5\)? – Aditya Agarwal · 8 months, 3 weeks ago

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– Timothy Wan · 8 months, 3 weeks ago

It's an error. Just corrected the note. Sorry!Log in to reply

Have you read the remainder factor theorem? If so, how do you think this could apply? – Calvin Lin Staff · 8 months, 3 weeks ago

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– Aditya Agarwal · 8 months, 3 weeks 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)Log in to reply

– Calvin Lin Staff · 8 months, 3 weeks 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.Log in to reply

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? – Timothy Wan · 8 months, 3 weeks ago

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– Anupam Nayak · 8 months, 2 weeks ago

You got confused between \(f(x)\) and \(r(x)\).Log in to reply