When the polynomial f(x)=x^32+3x^21-2 is divided by x-1 , the quotient and remainder are Q(x)and R respectively. Find the remainder when Q(x) is divided by x+1. How do you solve this ?

1 Answer
Jun 24, 2017

3

Explanation:

f(x)=(x-1)Q(x)+r_1 then

f(1)=1^32+3*1^21-2=2=r_1 then

Q(x)=(f(x)-r_1)/(x-1)=(x^32+3x^21-4)/(x-1),

Now Q(x)=(x+1)P(x)+r_2 then

Q(-1)=((-1)^32+3(-1)^21-4)/(-1-1) = 3=r_2