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Polynomial Functions

Let P x be a ...

Question

Let $P (x)$ be a polynomial, which when divided by $x - 3$ and $x - 5$ leaves remainders $10$ and $6$ respectively. If the polynomial is divided by $(x - 3) (x - 5)$ then the remainder is

- 2 x + 16

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16

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2 x - 16

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60

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Solution

The correct option is A $- 2 x + 16$
Let the remainder be, $a x + b$
From the given data,
$P (x) = (x - 3) (x - 5) q (x) + (a x + b)$

When $x = 3$ , $P (3) = 10$
and when $x = 5$ , $P (5) = 6$
The remainder is,
$3 a + b = 10$
$5 a + b = 6$

Solving the above equations,
$a = - 2, b = 16$
Thus, the remainder is, $- 2 x + 16$ .

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Let P(x) be a polynomial, which when divided by x−3 and x−5 leaves remainders 10 and 6 respectively. If the polynomial is divided by (x−3)(x−5) then the remainder is

The correct option is A −2x+16Let the remainder be, ax+b From the given data, P(x)=(x−3)(x−5)q(x)+(ax+b) When x=3, P(3)=10 and when x=5, P(5)=6 The remainder is, 3a+b=10 5a+b=6 Solving the above equations, a=−2,b=16 Thus, the remainder is, −2x+16.

Let $P (x)$ be a polynomial, which when divided by $x - 3$ and $x - 5$ leaves remainders $10$ and $6$ respectively. If the polynomial is divided by $(x - 3) (x - 5)$ then the remainder is