Question

Write a linear factorization of the function F(x)=x^4 + 49x^2

Answer 1

B) f(x) = x²(x+7i)(x-7i)

1) Let's start applying the factorization for that function

`\begin{gathered} f(x)=x^4+49x^2 \\ f(x)=x^2(x^2+49) \\ \end{gathered}`

2) Since the result of this quadratic incomplete equation: x² +49 is x1 = -7i and x_2= 7i let's rewrite it placing the factors, that zero the

`f(x)=x^2(x\text{ +7i)(x-7i)}`

Since distributing back we'll get to the original function.