Remainder theorem when we divide a polynomial f(x) by x − c the remainder r equals f(c)
Let’s say
f (x) ÷ (x − c) = q(x) + r
where r is the remainder. We also know
f (x) = (x − c)q(x) + r
If we now substitute x with c
f (c) = (c − c)q(c) + r
but c − c = 0, therefore
f (c) = r
Factor theorem when f (c) = 0 then x − c is a factor of the polynomial