Final answer:
To find the complex zeros of the polynomial function and write it in factored form, we can use the quadratic formula. For the given polynomial function, the discriminant is negative, indicating the roots are complex. Therefore, the polynomial has no real zeros. The complex zeros can be expressed as ± √(-13 ± i√3).
Step-by-step explanation:
To find the complex zeros of the polynomial function f(x) = x^4 + 13x^2 + 26 and write it in factored form, we can first try to factor out any common factors.
However, in this case, there are no common factors we can factor out. Therefore, we can use the quadratic formula to find the zeros, which is applicable for polynomials of degree 2. The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
For the given polynomial function, a = 1, b = 0, and c = 26. Substituting these values in the formula, we can find the complex zeros. However, upon performing the calculation, we find that the discriminant (b^2 - 4ac) is negative, which means the roots are complex. Therefore, the polynomial has no real zeros. The complex zeros can be expressed as:
x = ± √(-13 ± i√3)