Question

Find the monic polynomial, p(x) of degree 3 which has a remainder of -1 when divided by x-1, a remainder of 1 when divided by x+1 and p(0) = 1

Answer 1

\[p(x)=ax^3+bx^2+cx+1\]

Answer 2

yeah... i know that but i cant do the rest

Answer 3

long division?

Answer 4

no

Answer 5

since
If a polynomial p(x) is divided by (x-r), then the remainder is a constant given by p(r) .
\[p(1)=-1,p(-1)=1\]

Answer 6

\[a+b+c+1=-1\]
\[-a+b-c+1=1\]