Question

On dividing polynomial x4 + 2x3 -3x2+x-1 by g(x), the quotient and remainder were
x3+4x2+5x+11 and 21, respectively. Find g(x).​

Answer 1

Answer:

for finding the remainder we need to use remainder theorom

let p(x)=x

2

+2x+1

Here, the divisor is x+1 for dividend p(x), we need to equate it to 0 and put that value of x in p(x).

−x+1=0

∴x=−1

p(−1)=(−1)

2

+2(−1)+1=0

Hence, remainder=0