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
-1
x-(-1)
-1
x-(-1)
2i
x-2i
-2i
x-(-2i)
Polynomial
f(x)= [x-(-1)] [x-(-1)] (x-2i)[x-(-2i)]
Let's simplify the polynomial by applying the Distributive Property. For simplicity, we will start by multiplying the first two factors and the last two factors separately.
[x-(-1)] & * [x-(-1)]
(x-2i) & * [x-(-2i)]
After we find these products, we will multiply the obtained expressions.
