We can use the graphing techniques to sketch the graph of a polynomial.

Find the zeroes of a polynomial or the roots of the polynomial equation to sketch its graph.

For example, sketch the graph of the polynomial

First, we write the polynomial *P(x)* as a product of its factors:

Then we find the *x*-intercepts: *y*=0

So the *x*-intercepts are 0, -3 and 2.

For *y*-intercepts: *x*=0

So the *y*-intercept is 0.

We look at which part of the graphs are above and which are below the *x*-axis between the *x*-intercepts.

Test 1) *x*=-4 (less than -3)

So the curve is below the *x*-axis.

Test 2) *x*=-1 (between -3 and 0)

So the curve is above the *x*-axis.

Test 3) *x*=1 (between 0 and 2)

So the curve is below the *x*-axis.

Test 4) *x*=3 (more than 2)

So the curve is below the *x*-axis.

Then by the information above, we can sketch the graph: