Week 1: Polynomials – Day 3

1. Make a quick sketch of the function:       f(x) = x2 – 4.

2. Make a quick sketch of the function:       g(x) = (4 – x)2.

3. Let h(x) = f(x)*g(x) = (x2 – 4)( 4 – x)2 . What kind of function is h(x)?

4. How many roots does h(x) have?

5. Make a quick sketch of the graph of h(x). Hint: you can find all the real roots of h(x). Test the values of points between and around the roots; e.g. h(-3), h(0), h(3), h(5).

Week 1: Polynomials – Day 1

1. If P(x) is a polynomial of degree 7, and Q(x) is a polynomial of degree 2, what kind of function is f(x) = P(x)*Q(x)?

2. Let P(x) be a polynomial of degree 7. What is the highest number of real roots (zeroes) that P(x) could have?

3. Let P(x) be a polynomial function of degree 7. What is the lowest number of real roots (zeroes) that P(x) could have?

4. Let Q(x) be a polynomial function of degree 4. What is the lowest number of real roots (zeroes) that Q(x) could have?

5. Let f(x) = P(x) = x*x*x*x*(x – 1)*(x – 2)*(x – 3). How many distinct real roots does f(x) have?