## Math 098 - Chapter 5&6 Study Guide

1. 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.
2. Use substitution to solve a 2x2 system of linear equations. Look at problems 5.1.47-57.
3. Use the addition technique to solve a 2x2 system of linear equations. Look at problems 5.2.23-43.
4. Use your calculator to evaluate a determinant. Look at problems 5.5.17-23.
5. Use Cramer's Rule to solve a 2x2 system of linear equations. Look at problems 5.5.43-53.
6. 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).
7. 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.
8. 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.
9. Factor the special products completely. Four parts. Look at problems 6.4.17-27, 31-71.
10. Factor the polynomial completely. Three parts. Look at problems 6.5.23-77.
11. 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.
12. Determine the quotient using long division. Look at problems 6.7.25-39.
13. Use synthetic division to determine the quotient and remainder. Look at problems 6.8.3-19.
14. Use synthetic division to evaluate a polynomial. Look at problems 6.9.3-11.
15. 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