Factor theorem and proof
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Gaurav Seth 5 years, 3 months ago
Consider a polynomial f(x) which is divided by (x-c), then f(c)=0.
Using remainder theorem,
f(x)= (x-c)q(x)+f(c)
Where f(x) is the target polynomial and q(x) is the quotient polynomial.
Since, f(c) = 0, hence,
f(x)= (x-c)q(x)+f(c)
f(x) = (x-c)q(x)+0
f(x) = (x-c)q(x)
Therefore, (x-c) is a factor of the polynomial f(x).
Another Method
By <a href="https://byjus.com/maths/remainder-theorem/">remainder theorem</a>,
f(x)= (x-c)q(x)+f(c)
If (x-c) is a factor of f(x), then the remainder must be zero.
(x-c) exactly divides f(x)
Therefore, f(c)=0.
The following statements are equivalent for any polynomial f(x)
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