Let's start by solving the first part of the exercise, which asks to find the degree of each polynomial.

1. Find the degree of each of the following polynomials:

• a. $3x^2 + 12x - 1$

  • The degree of a polynomial is the highest power of $x$. Here, the highest power is $2$ (from $3x^2$).
  • Degree: $2$

• b. $5x^3 + 8$

  • The highest power of $x$ is $3$ (from $5x^3$).
  • Degree: $3$

For the remaining parts (c through f), we would need the functions $f(x)$, $g(x)$, and $h(x)$ to proceed with the evaluations. Could you provide those functions, or should I assume general forms for them?

Would you like further details on polynomial degrees or have any questions?

Here are 5 related questions for deeper understanding:

1. What is the degree of a constant polynomial like $h(x) = 7$?
2. How do you determine the degree of a polynomial when it's written in factored form?
3. Can a polynomial have a degree of zero?
4. How does the degree of a polynomial affect its graph?
5. What happens to the degree of a polynomial when you multiply two polynomials together?

Tip:

The degree of a polynomial gives us important information about the behavior of its graph, particularly its end behavior and the number of possible roots (real or complex).