Question

select the correct answer from each drop - down menu.
how many solutions does each polynomial have?

equation	number of solutions
$y = 2x^5 - x^4 + 2x^3 - 6x^2 + 2x + 4$
$y = - 4x^3 - 10x^2 + 7x + 5$

Explanation:

Step1: Identify degree of linear polynomial

The polynomial $y = -6x - 9$ is degree 1.

Step2: Apply Fundamental Theorem of Algebra

A degree $n$ polynomial has $n$ complex solutions. For $n=1$: $1$ solution.

Step3: Identify degree of 5th-degree polynomial

The polynomial $y = 2x^5 - x^4 + 2x^3 - 6x^2 + 2x + 4$ is degree 5.

Step4: Apply Fundamental Theorem of Algebra

For $n=5$: $5$ solutions.

Step5: Identify degree of 3rd-degree polynomial

The polynomial $y = -4x^3 - 10x^2 + 7x + 5$ is degree 3.

Step6: Apply Fundamental Theorem of Algebra

For $n=3$: $3$ solutions.

Answer:

1. For $y = -6x - 9$: 1
2. For $y = 2x^5 - x^4 + 2x^3 - 6x^2 + 2x + 4$: 5
3. For $y = -4x^3 - 10x^2 + 7x + 5$: 3