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

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 (A) -2x + 16 (B) 16 (C) 2x - 16 (D) 60

Tardigrade Admin · Accepted Answer

∵ P(x)=(x-3)(x-5) =Q(x)+(a x +b) Given, P(3)=10 and P(5)=6 ⇒ 3 a +b=10 ...(i) and 5 a +b=6 ...(ii) On solving Eqs. (i) and (ii), we get a=-2 and b=16 ∴ Remainder =-2 x +16

Q. 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

$- 2 x + 16$

$16$

$2 x - 16$

$60$

$∵ P (x) = (x - 3) (x - 5)$
$= Q (x) + (a x + b)$
Given, $P (3) = 10$ and $P (5) = 6$
$\Rightarrow 3 a + b = 10$ ...(i)
and $5 a + b = 6$ ...(ii)
On solving Eqs. (i) and (ii), we get
$a = - 2$ and $b = 16$
$∴$ Remainder $= - 2 x + 16$

Q. 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

−2x+16

16

2x−16

60