Question

Use a graph of a polynomial G(x) to determine its zeros and the multiplicity of each zero. List the zeros from smallest to largest.

Answer 1

Zeros of a Polynomial

When a polynomial has a zero at x = a, then its graph 'touches' or 'crosses' the x-axis. If the zero has an even multiplicity (2, 4, 6, etc.), the graph 'bounces' off the x-axis.

We can see the graph crosses the x-axis 4 times and no bouncing occurs, so each zero has a multiplicity of 1.

From left to right, the zeros are:

x = -4 with a multiplicity of 1.

x = -2 with a multiplicity of 1.

x = 1 with a multiplicity of 1.

x = 3 with a multiplicity of 1.