Question

On dividing 2x3–x2–9x + 13 by a polynomial g(x), the quotient and remainder were (x–2) and(x+ 5) respectively. Find g(x)

Answer 1

Answer:

g (x) = 2x2 +3x -4

This answer will get subtracting remainder from polynomial and then dividing it by quotient

Answer 2

Answer:

dividend = 2x³-x²-9x+3

divisor = g(x)

quotient= (x-2)

remainder = (x+5)

using division algorithm

D= d×Q+r

(Dividend= Divisor×Quotient+Remainder)

2x³-x²-9x+3 = g(x)×(x-2) +(x-5)

2x³-x²-9x+3-(x-5) = g(x).(x-2)

2x³-x²-9x+3-x+5 = g(x).(x-2)

2x³-x²-10x+8 = g(x).(x-2)

g(x) = 2x³-x²-10x+8/x-2

g(x) = 2x²+3x-4(answer)

*Note - For division refer the attachment.