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
-2
x-(-2)
-3
x-(-3)
4-3i
x-(4-3i)
4+3i
x-(4+3i)
Polynomial
f(x)= [x-(-2)] [x-(-3)] [x-(4-3i)][x-(4+3i)]
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-(-2)] & * [x-(-3)]
[x-(4-3i)] & * [x-(4+3i)]
After we find these products, we will multiply the obtained expressions.
