If a is a zero of f(x)=0, then (x-a) is a factor of f(x).
If f(x) is a polynomial with real coefficients, then the complex roots of f(x)=0 occur in conjugate pairs.
If f(x) is a polynomial with real coefficients, then the complex roots of f(x)=0 occur in conjugate pairs.
This theorem states that if a + bi is a complex root, then a- bi is also a zero. Additionally, recall that if a is a zero of f(x)=0, then (x-a) is a factor of f(x).
Root
Factor
-4
x-(-4)
4+i
x-(4+i)
4-i
x-(4-i)
Polynomial
f(x)= [x-(-4)] [x-(4+i)] [x-(4-i)]
Let's simplify the polynomial by applying the Distributive Property. For simplicity, we will start by multiplying the first two factors and then we will multiply the result by the last factor.
