Question

week 2 discussion

hi everyone, and welcome to week 2 of math 102!

for this discussion i would like to reflect on the exam.

1. was the exam easier or more difficult than you expected?
2. what did you do well on in preparing for the exam?
3. what can do do better next time in preparing for the exam?
4. which of the following functions are polynomials?

a. (f(x) = 3 - 5x - 4x^2 + x^3 + 8.2x^4)
b. (g(x) = \frac{1}{2x+5})
c. (h(x) = \sqrt{5x-7})
d. (a(x) = -3)
e. (b(x) = 2x + 1)
f. (c(x) = |2x - 5|)
g. (p(x) = x^3 + x^2 + x + 1 + x^{-1} + x^{-2})
h. (q(x) = -x^7)

1. for each of the above that is a polynomial, can you find the
2. degree?
3. lead coefficient?
4. lead term?

Explanation:

Step1: Identify polynomial functions

Polynomials have non-negative integer exponents.
A, D, E, H are polynomials.

Step2: Analyze function f(x)

$$f(x) = 8.2x^4 + x^3 - 4x^2 - 5x + 3$$

Degree is \(4\), lead coefficient is \(8.2\), lead term is \(8.2x^4\).

Step3: Analyze function a(x)

$$a(x) = -3$$

Degree is \(0\), lead coefficient is \(-3\), lead term is \(-3\).

Step4: Analyze function b(x)

$$b(x) = 2x + 1$$

Degree is \(1\), lead coefficient is \(2\), lead term is \(2x\).

Step5: Analyze function q(x)

$$q(x) = -x^7$$

Degree is \(7\), lead coefficient is \(-1\), lead term is \(-x^7\).

Answer:

The polynomial functions are:
A. \(f(x) = 3 - 5x - 4x^2 + x^3 + 8.2x^4\)
D. \(a(x) = -3\)
E. \(b(x) = 2x + 1\)
H. \(q(x) = -x^7\)

For each polynomial function:

• For \(f(x) = 3 - 5x - 4x^2 + x^3 + 8.2x^4\):

1. Degree: \(4\)
2. Lead Coefficient: \(8.2\)
3. Lead Term: \(8.2x^4\)

• For \(a(x) = -3\):

1. Degree: \(0\)
2. Lead Coefficient: \(-3\)
3. Lead Term: \(-3\)

• For \(b(x) = 2x + 1\):

1. Degree: \(1\)
2. Lead Coefficient: \(2\)
3. Lead Term: \(2x\)

• For \(q(x) = -x^7\):

1. Degree: \(7\)
2. Lead Coefficient: \(-1\)
3. Lead Term: \(-x^7\)