Question

on dividing _x2+3x2-3x+5 by a polynomial get(x), the quotient and remainder were (x-2) and 3 respactively.find get(x).
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Answer 1

Answer:

dividend=quotient×divisor+remainder

divisor=(dividend-remainder)/quotient

=(x^3+3x^2-3x+5-3)/x-2

=(x^3+3x^2-3x+2)/x-2

=(x^3+3x^2-3x+2)/x-2

check ur dividend in ur question I think u write wrongly

Answer 2

Given :p(x) = 3x²-x³-3x+5

quotient = x-2

remainder = 3

To find : g(x)

Solution :

p(x) = -x³+3x²-3x+5

using the remainder theorem

p(x) = g(x)× quotient + remainder

-x³+3x²-3x+5  = g(x) × (x-2) + 3

-x³+3x²-3x+5 -3 = g(x) × (x-2)

g(x) = $\frac{-x^3+3x^2-3x+5 -3}{x-2}$

on dividing we get

g(x) = -x²+x-1

hence , The value of g(x) is  -x²+x-1

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