# If p(x)=x^4-2x^3+3x^2-ax+b is a polynomial such that when it is divided by x-1 and x+1 the remainders are respectively 5 and 19 .determine the remainder when p(x) is divided by(x-2).find 'a' and 'b'

2
by tssuyambulingam

2015-04-28T16:19:33+05:30
Remainder = 10
a = 5
b = 8
where is the explanation............ and the steps.................
2015-04-29T02:45:37+05:30

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P(x) = x⁴ - 2 x³ + 3 x² - a x + b

reminder of the polynomial when divided by (x - k)  is  P(k). substitute  k in place of x.

P(1) = 5  =>  1 -2  +3 - a + b = 5
b - a = 3

P(-1)  = 19  =>  1 +2 + 3 + a + b = 19
a + b = 13
adding the two equations we get:    2 b = 16  => b = 8
a = 5

reminder when P(x) is divided by  (x-2) :
=  P(2)
= 2^4 - 2 2^3 + 3  2^2 - 5 * 2 + 8
=  10

thank you so much