Learning Resources
Outcomes
By the end of this lesson you will be able to answer questions like the ones in the pre-test below.
Approach #1
Answer the questions on the pre-test below in your Math 3103 binder. Then refer to the pages of the lesson that contain instruction on the questions you were unable to do, for which you got an incorrect answer, or for which you would like some further explanation.
Approach #2
Proceed directly to the first page of the lesson without attempting the pre-test. To do this simply click on the Lesson button above. You can then return to this pre-test later and use it as a worksheet.
Pre-test
1. What are the possible rational roots of the equation x3 - 2x - 21 = 0 ?
2. Does x + 2 divide evenly into 2x3 + x2 + 3x + 7 ? Explain how you know.
3. Explain what is meant by a depressed equation.
4. How many roots (real or imaginary) must a polynomial of degree 100 have? Why?
5. What is the remainder when 2x3 + x2 + x + 7 is divided by x + 2 ?
6. When the polynomial p(x) is divided by x - 2, the quotient is 2x2 - x + 3 and the remainder is 5. Find the polynomial p(x).
7. Find all the roots, real and imaginary, of the following equations.
(a) x3 - 2x2 - 5x + 6 = 0 (b) 12x3 + 20x2 - x - 6 = 0
(c) x4 + x3 + 2x2 + 4x - 8 = 0
Students will be expected to:
- Recognize and use the language of polynomials.
- Solve linear equations.
- Factor polynomial expressions.
- Use factoring to solve polynomial equations in one variable of degree four or less.
- Use the rational roots theorem to help solve polynomial equations in one variable of degree four or less.
- Use synthetic division in connection with the rational roots theorem to obtain a depressed equation.
Prerequisites
To be successful in this lesson, it would be helpful to know the following:
- How to divide polynomials.
- The terms quotient, dividend, divisor, remainder.
- The meaning of the root of an equation.
- The meaning of the zero of a function.
- How to verify if a number is a zero of a function.