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Polynomial Functions

Let Px 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 B $- 2 x + 16$
Given, $P (x) = (x - 3) (x - 5)$ $Q (x) + (a x + b)$
Also given, $P (3) = 10$ and $P (5) = 6$
$\Rightarrow 3 a + b = 10$ ...(i)
And $5 a + b = 6$ ...(ii)
Subtracting both the equations, we get
$a = - 2$
Putting this value in equation (i) we get
$3 (- 2) + b = 10$
$\Rightarrow b = 10 + 6$
$\Rightarrow b = 16$
Thus $a = - 2$ and $b = 16$
Therefore, remainder $- 2 x + 16$ .

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Similar questions

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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 B −2x+16Given, P(x)=(x−3)(x−5)Q(x)+(ax+b)Also given, P(3)=10 and P(5)=6⇒3a+b=10 ...(i)And 5a+b=6 ...(ii)Subtracting both the equations, we geta=−2Putting this value in equation (i) we get3(−2)+b=10⇒b=10+6⇒b=16Thus a=−2 and b=16Therefore, remainder −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