## Math 098 - Chapter 5&6 Study Guide

- Describe the three possible solutions to a system of linear equations. Know the graphical
distinction (parallel lines, coincident lines, intersecting lines); whether the system is consistent
or inconsistent; if the system is consistent, whether the system is dependent or independent.
Look in your lecture notes.
- Use substitution to solve a 2x2 system of linear equations. Look at problems 5.1.47-57.
- Use the addition technique to solve a 2x2 system of linear equations. Look at problems
5.2.23-43.
- Use your calculator to evaluate a determinant. Look at problems 5.5.17-23.
- Use Cramer's Rule to solve a 2x2 system of linear equations. Look at problems 5.5.43-53.
- Use your calculator and matrices to solve a system of linear equations. Show the matrices
entered into the calculator and the expression evaluated to get the answer. This is the one
that's not covered in the book. If A = coefficient matrix and B = right hand side, then the
equation can be written as AX=B and the solution is X = A
^{-1}*B (the inverse of matrix A times
matrix B).
- Perform the indicated operation and simplify the results. Addition, subtraction, and
multiplication of polynomials, including special products. Eight parts. Look at problems
6.1.57-63, 89-101; 6.2.13-39, 47-61, 87-99.
- Factor the given expressions by factoring out the greatest common factor or by grouping.
Three parts. Look at problems 6.3.29-33, 37-55, 63-65.
- Factor the special products completely. Four parts. Look at problems 6.4.17-27, 31-71.
- Factor the polynomial completely. Three parts. Look at problems 6.5.23-77.
- Solve the equation by factoring. Remember that one side must equal zero in order for the
factors to equal zero. Three parts. Look at problems 6.6.27-53, 57-63.
- Determine the quotient using long division. Look at problems 6.7.25-39.
- Use synthetic division to determine the quotient and remainder. Look at problems 6.8.3-19.
- Use synthetic division to evaluate a polynomial. Look at problems 6.9.3-11.
- Use synthetic division, the given factor, and the factor theorem to factor the polynomial
completely. Look at problems 6.9.37-47

### Notes:

- All problems with the exception of #6 are directly from the odd exercises in the text

**Point totals for the problems:**

1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
Total |

6 |
5 |
5 |
3 |
5 |
4 |
16 |
9 |
12 |
9 |
9 |
3 |
3 |
3 |
3 |
95 |