Factor the polynomial function over the complex numbers. f(x)=x4+9x3+15x2+9x+14 Enter your answer in the box. f(x)=

The polynomial function

can be factored over the complex numbers as follows

The constant term of the fourth degree polynomial

is positive, and has the factors and . So, we will try out polynomial division with

so is a factor.

Try out the polynomial division again, this time dividing the quotient with

so is also a factor.

So far, we have factored the fourth degree polynomial as follows

we can still factor further by arranging it as a difference of two squares

So, our final factorization of the polynomial function is

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