Two Baby Facts and a Key Fact
Remainder Theorem: If a polynomial 𝑓𝑥 is divided by 𝑥−𝑘, then then the remainder is 𝑓𝑘.
A polynomial 𝑔𝑥 is a factor of 𝑓𝑥 if 𝑓𝑥𝑔𝑥 has a remainder of 0.
Factor Theorem: 𝑓𝑐=0⟺𝑥−𝑐 is a factor of 𝑓𝑥