To determine if a given liinear polynomial X-a is a factor of f(x) we need to check wheather
- f(x) =0
- f(0) = 0
- f(a) = 0
- f(a) = 1
Explanation
To determine if a given linear polynomial x−a is a factor of a polynomial f(x), we need to check whether f(a)=0. This is based on the Factor Theorem, which states that n
x−a is a factor of f(x) if and only if f(a)=0.
Here are the steps to check if f(x) at x = a is a factor of f(x):
- Evaluate f(x) at x=a: Substitute a into the polynomial f(x).
- Calculate f(a).
- Check the result:
f(a)=0, then x−a is a factor of f(x).
f(a) is not equal to 0, then x−a is not a factor of f(x)
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