Degree
Highest exponent of the variable in a polynomial.
π‘ Degree = Biggest power
Leading Coefficient
Coefficient of the highest-degree term.
π‘ Front number of biggest term
Root = Zero
A value of x making f(x) = 0.
π‘ Root = Zero = x-intercept
Factor Theorem
(x β a) is a factor βΊ f(a) = 0
π‘ Zero in β factor out
Remainder Theorem
Remainder of f(x) Γ· (x β a) equals f(a)
π‘ Plug a in β get remainder
Multiplicity
How many times a root is repeated as a factor.
π‘ Evenβtouches, Oddβcrosses
Monic Polynomial
Leading coefficient = 1.
π‘ mono = one β front coeff is 1
Conjugate Pairs
Complex roots of real polynomials come as aΒ±bi pairs.
π‘ Always paired β never alone