Question

Given the zeros of polynomial $P$ and list their multiplicities:
$P\left(x\right)=(x+1)(x+2)+(x+1){(x+2)}^2$

Answer 1

A polynomial is a function of the form $f\left(x\right)=a_n{x}^n+a_{n-1}{x}^{n-1}+...+a_2{x}^2+a_{1}x+a_0$

where $a_n,a_{n-1},...a_2,a_1,a_0$ are constants and $n$ is a natural number.

To get Zeroes of the polynomial take $f\left(x\right)=0$

Now given that

$P\left(x\right)=(x+1)(x+2)+(x+1)(x+2{)}^2$

or $P\left(x\right)=(x+1)(x+2)(x+3)$

Zeroes of $P\left(x\right)$ are $-1,-2,-3$

The zero $-2$ has multiplicity $1$,

Zero $-1$ has multiplicity $1$, and

Zero $-3$ has multiplicity $1$.