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Question

# A quadratic polynomial when divided by (x+2) leaves a remainder 1, and when divided by (xâˆ’1), leaves a remainder 4. What will be the remainder if it is divided by (x+2)(xâˆ’1)?

A
1
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B
4
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C
(x+3)
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D
(x3)
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Solution

## The correct option is D (x+3)Let the quadratic polynomial be denoted as P(x).The polynomial when divided by x+2 gives a remainder of 1. So, from remainder theorom, P(−2)=1.Similarly, the polynomial when divided by x−1 gives a remainder of 4. So, from remainder theorom, P(1)=4.Now, if P(x) is divided by the product (x+2)(x−1), the remainder can be at most be a linear function.We can write P(x)=C(x+2)(x−1)+(Ax+B), where A, B, and C are constants.Use P(1)=4 and P(−2)=1. We get two equations: A+B=1 and −2A+B=1.Solving, we get A=1 and B=3. Hence, the remainder is Ax+B=x+3

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