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Remainder Theorem

16. Let p(x)b...

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16. Let p(x)be a polynomial,when divide by (x-19) gives 91 as a remainder and when divided by (x-91) gives 19 as remainder.Find the remainder when p(x) is divided by (x-19) (x-91).

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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)

p (x)

be a polynomial such that when

p (x)

(x - 19)

, the remainder is

99

p (x)

(x - 99)

, the remainder is

19

. The remainder when

p (x)

(x - 19) (x - 99)

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 number when divided by

53

33

as quotient and

19

as remainder. Find the number.

The polynomial $x^{4}$ - 2 $x^{3}$ + 3 $x^{2}$ - ax + b when divided by (x+1) and (x-1) gives remainders 19 and 5 respectively. Find the remainder when the polynomial is divided by (x-3).

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