Question 1 (2 points) Using the Fundamental Theorem of Algebra, how many roots/solutions should the polynomial have? \( f(x)=x^{4}+2 x^{3}-6 x^{2}+4 x-16 \) 4 6 3

The Fundamental Theorem of Algebra tells us that a polynomial of degree n will have exactly n roots, counting multiplicities. In this case, your polynomial \( f(x) = x^{4} + 2x^{3} - 6x^{2} + 4x - 16 \) is a degree 4 polynomial, which means it will have 4 roots or solutions, either real or complex. Now, here’s a fun fact: the number of roots can be visualized with a graph! When you plot the polynomial, the intersections with the x-axis represent the real roots. So, not only does the theorem give you a number, but it's also a gateway to exploring the polynomial's behavior visually.