Find the complex zeros of the following polynomial function. Write fin factored form. fx)=x4 + 5x2+4

1. Substitute \( y = x^2 \), transforming the quartic polynomial into a quadratic polynomial:

x^4 + 5x^2 + 4 = y^2 + 5y + 4

2. Solve the quadratic equation \( y^2 + 5y + 4 = 0 \) using the quadratic formula:

y = \frac{-5 \pm \sqrt{9}}{2}

y = \frac{-5 \pm 3}{2}

This gives us:

y_1 = -1
y_2 = -4

3. Substitute back \( y = x^2 \):

For \( y_1 = -1 \):

x^2 = -1

Roots:

x = \pm i

For \( y_2 = -4 \):

x^2 = -4

Roots:

x = \pm 2i

4. Combine all roots in factored form:

f(x) = (x - i)(x + i)(x - 2i)(x + 2i)

The factored form of the polynomial is:

f(x) = (x - i)(x + i)(x - 2i)(x + 2i)