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Remainder Theorem

Let p(x) be a...

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Let p(x) be any polynomial of x , which leaves remainder a,b,c when divided by (x-a),(x-b),(x-c).what will be the remainder when p(x) divided by (x-a)(x-b)(x-c)

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Q. Let p(x) be a polynomial of degree more than 2. When p(x) is divided by x-2, it leaves remainder 1 and when it is divided by x-3, it leaves remainder 3. Find the remainder, when p(x) is divided by (x-2)(x-3).

p (x)

be any polynomial. When it is divided by

(x - 19)

(x - 91)

, then the remainders are

91

19

respectively. The remainder, when

p (x)

(x - 19) (x - 91)

Q. Let p(x) be a quadratic polynomial such that

p (0) = 1

. If p(x) leaves remainder

4

when divided by

x - 1

and it leaves remainder

6

when divided by

x + 1

; then which one is correct?

Q. A polynomial

p (x)

when divided by

(x - 3),

leaves a remainder of

5.

p (x)

(x - 5),

the remainder is

3.

r (x)

be the remainder when

p (x)

(x - 3) (x - 5) .

Then the value of

r (1)

p (x)

be a quadratic polynomial with constant term

1

p (x)

, when divided by

x - 1

leaves remainder

2

and when divided by

x + 1

leaves remainder

4

. Then the sum of the roots of

p (x) = 0

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