Question

Give the zeros of polynomial and list their multiplicities:
$P\left(x\right)=(x+2)(x-1)$

Answer 1

The zeroes of a polynomial function $p\left(x\right)$ are the x-values that yield $0$ as the function's value. That is, the zeros of the polynomial $p\left(x\right)$ are the roots, or solutions, to the equation $p\left(x\right)=0$. Zeros are also called the x-intercepts of the polynomial, or points where the graph of the polynomial touches the x-axis.

From the factor theorem, we know that when $c$ is a zero of the polynomial $p\left(x\right)$, then $x-c$ is a factor of $p\left(x\right)$. The multiplicity of the number of factors of $x-c$ in the linear factorisation of $p\left(x\right)$.

Hence, polynomial $P\left(x\right)=(x+2)(x-1)$ has the zero $-2$ with multiplicity $1$ and the zero $1$ with multiplicity $1$.