Refresher - Zeros and Zero of Multiplicity K

Refresher

Zeros

A zero or root of a polynomial function is the value of x such that ${\displaystyle f\left(x\right)=0}$. In other words roots (solutions, or zeros) are the x-intercepts.

Zero of multiplicity k

If ${\displaystyle {(x-r)}^k}$ is a factor of a polynomial function f and ${\displaystyle {(x-r)}^{k+1}}$ is not a factor of f, then r is called a zero of multiplicity of ${\displaystyle k}$.

In other words, when a polynomial function is set equal to zero and has been completely factored and each different factor is written with the highest appropriate exponent, depending on the number of times that factor occurs in the product, the exponent on the factor that the zero is a solution for, gives the multiplicity of that zero. The exponent indicates how many times that factor would be written out in the product, this gives us a multiplicity