# GRE Subject Test: Math : Fundamental Theorem of Algebra

## Example Questions

### Example Question #1 : Fundamental Theorem Of Algebra

Explanation:

The corollary to the Fundamental Theorem of Algebra states that for any polynomial the number of solutions will match the degree of the function.

The degree of a function is determined by the highest exponent for x, which in this case is 7.

This means that there will be 7 solutions total for the below function.

This means that max number of REAL solutions would be 7, but the total number of solutions, real, repeated or irrational will total 7.

### Example Question #12 : Polynomials

Explanation:

In order to determine the correct answer, we must first change the function to be in standard form. A function in standard form begins with the largest exponent then decreases from there.

We must change:

to become:

Once we have established standard form, we can now see that this is a degree 3 polynomial, which means that it will have 3 roots or solutions.

### Example Question #21 : Polynomials

Explanation:

If a complex or imaginary root exists, its' complex conjugate must also exist as a root.