Question

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 ?

Answer 1

`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`