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*f (c) = (c − c)q(c) + r*
**Factor theorem** when f (c) = 0 then x − c is a factor of the polynomial
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April 13, 2024

**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

but c − c = 0, therefore

f (c) = r

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