WBJEE · Maths · Basic of Mathematics
Let \(P(x)\) be a polynomial, which when \(\begin{array}{llll}\text { divided by } & (x-3) & \text { and } & (x-5) & \text { leaves }\end{array}\) remainders 10 and 6, respectively. If the polynomial is divided by \((x-3)(x-5),\) thes the remainder is
- A \(-2 x+16\)
- B 16
- C \(2 x-16\)
- D 60
Answer & Solution
Correct Answer
(A) \(-2 x+16\)
Step-by-step Solution
Detailed explanation
\(\because P(x)=(x-3)(x-5)\) \(=O(x)+(a x+b)\) Given, \(\quad P(3)=10\) and \(P(5)=6\) \(\Rightarrow \quad 3 a+b=10\) and \(\quad 5 a+b=6\) On solving Bqs. (i) and (ii), we get \(a=-2\) and \(b=16\) \(\therefore\) Remainder \(=-2 x+16\)
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