Polynomial Functions & Zeros
Zeros are where the graph crosses the x-axis. Factor to find them.
The rules
- Set f(x) = 0 and factor.
- A factor (x − r) gives a zero at x = r.
- The number of zeros of a degree-n polynomial is at most n.
- A repeated factor means the graph touches the axis and turns around.
Watch out: Taking the sign from the factor instead of reversing it.
Worked example
What are the zeros of f(x) = (x + 2)(x − 5)?
- Set each factor to 0.
- x + 2 = 0 gives −2, and x − 5 = 0 gives 5.
Answer: −2 and 5
Try it yourself
Practice questions for this skill are for signed-in students. A free account is all you need.