Question

Find a polynomial $f(x)$ of degree $5$ such that both of these properties hold:

$\bullet$ $f(x)$ is divisible by $x^3$.

$\bullet$ $f(x)+2$ is divisible by $(x+1)^3$.

Write your answer in expanded form (that is, do not factor $f(x)$).

Answer 1

Answer:

Step-by-step explanation:

f(x)=ax³

ax³+2=b(x+1)³

ax³+2=b(x³+3x²+3x+1)

(a-b)x³-3bx²-3bx-b=0