Given polynomial .
(a) To show that (x – 3) is a factor of f(x).
Factor theorem:
<em>A polynomial f(x) has a factor of (x – a), if and only if f(a) = 0.</em>
= 0
f(3) = 0
Hence (x – 3) is a factor of f(x).
(b)
Here is common in first 2 terms and 2 is common in next 2 terms.
Now, (x – 3) is common in both terms.
and
x = 3 and
3 is the real root.
using quadratic formula solve and find the other roots.
These are complex roots.
Hence 3 is the only real root of the equation f(x) = 0.