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Remainder Theorem

A polynomial ...

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A polynomial leaves remainder 5 when divided by (x-3) it also leaves remainder 7 when divided by (x-4). Find remainder when it divided by (x-3)(x-4)

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Similar questions

Q. The polynomial

p (x) = x^{4} - 2 x^{3} + 3 x^{2} - a x + 3 a - 7

when divided by

x + 1

leaves the remainder

19

.
Find the value of

a

. Also find the remainder when

p (x)

x + 2

.

Q. A polynomial

f (x)

leaves remainder

15

when divided by

(x - 3)

(2 x + 1)

when divided by

(x - 1)^{2}

f

(x - 3) (x - 1)^{2},

the remainder is

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).

Q. A quadratic polynomial when divided by

(x + 2)

leaves a remainder

1

, and when divided by

(x - 1)

, leaves a remainder

4

. What will be the remainder if it is divided by

(x + 2) (x - 1)

?

Q. Question 2
The polynomial

p (x) = x^{4} - 2 x^{3} + 3 x^{2} - a x + 3 a - 7

when divided by x + 1 leaves the remainder 19. Find the value of a. Also , find the remainder when p(x) is divided by x + 2.

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