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 roots of the equation: (x + 3)(3x - 1)(x + 2) = 0 ?
2. What root is common to both of the following equations? Explain why this root is common.
3x2 + 9x = 0 and 4x3 + 20x2 + 16x = 0
3. Find all roots, real or imaginary, of the following equations:
(a) 4x2 - 5x = 0 (b) 25x2 - 9 = 0
(c) x2 - 2x - 35 = 0 (d) 3x2 - 14x + 11 = 0
(e) 18x3 - 9x2 - 2x + 1 = 0 (f) x4 - 16 = 0
(g) 2x4 - 10x2 = - 8 (h) x(x - 1) = 2(x - 1)
(i) 6x2 + 11x = - 4 (j) x3 = 7x2 - 6x
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:
- The meaning of the root of an equation.
- How to factor polynomials.
- How to solve (find the root of) linear equations in one variable.