Practice Problems for Section 2.3 and 2.5 –Math 1111

Consider the following polynomial:

f(x) = x⁵ – 8x⁴ + 28x³ – 56x² + 64x – 32

1. What is the degree of the polynomial?
2. What is the leading coefficient, a_n ?
3. Use the Rational Root Test to list ALL possible rational zeros of the polynomial
4. Use synthetic division to find ALL the zeros of the polynomial, real and imaginary. Be sure to check for multiplicity of zeros.
5. Find the y-intercept. Write as an ordered pair.
6. Using the above information to sketch the graph of the polynomial below.

Consider the following polynomial function:

7. What is the degree of the polynomial?

8. What is the leading coefficient, a_n ?
9. Use the Rational Root Test to list ALL possible rational zeros of the polynomial
10. Use synthetic division to find ALL the zeros of the polynomial, real and imaginary. Be sure to check for multiplicity of zeros.
11. Find the y-intercept. Write as an ordered pair.
12. Using the above information to sketch the graph of the polynomial below.