04.05 Root Theorems
The Rational Root Theorem
The application of this theorem provides a list of all the possible rational
zeros of a function.
f(x)=3x3+x2+21x−11
Factors of p:±1and±11
Factors of q:±1and±3
Factors of P/q: ±1, ±11, ±1/3 and ± 11/3
The Fundamental Theorem of Algebra
The Fundamental Theorem of Algebra generally states that the degree of a
polynomial is equivalent to the number of zeros of a function, both real and
complex.
By the Fundamental Theorem of Algebra, the polynomial
function f(x)=x2−3x−28 has two zeros since the degree of the function is
two.
The Factor Theorem
The Factor Theorem states that the binomial divisor is a factor of the
function if the remainder is zero.
(f(x)=−4x3+21x2−25)÷(x−5)
The remainder is zero, making x - 5 a factor of the function.