# MAT-099 Objectives

## MAT-099 Intermediate Algebra

### Course Description

This course is a continuation of MAT-097, Foundations of Algebra. Topics in this course include polynomial arithmetic, introduction to functions, factoring, roots and radicals, rational expressions, absolute value inequalities, quadratic equations and the quadratic formula, and solving applied problems. This course does not satisfy degree requirements. PREREQUISITE: Grade of C or better in MAT-097, Foundations of Algebra or placement. Course may require an additional lab hour. Credit hours: 3.0.

### Learning Outcomes

1. Rewrite expressions by understanding and applying the concepts of combining like terms, the distributive property, and factoring
2. Write equivalent forms of equations and inequalities and solve them with fluency
3. Apply knowledge of a variety of types of equations, including linear, quadratic, rational, and radical equations, to solve real world problems

### Instructional Objectives

POLYNOMIALS

1. Define and identify: monomial, binomial, polynomial
2. State the degree of a term, the degree of a polynomial, and write a polynomial in descending powers of a variable
3. Find the sum and difference of two polynomials
4. Multiply a polynomial by a monomial or a binomial
5. Divide a polynomial by a monomial
6. Use long division to divide a polynomial by a binomial

FUNCTIONS

7. Understand the concepts of relation and function
8. Decide whether an equation defines a function
9. Use function notation
10. Apply the function concept in applications and graphing

FACTORING
11. Define and identify: factor, common factor, greatest common factor
12. Factor out the greatest common factor from a polynomial
13. Factor by grouping
14. Factor the difference of two squares as a sum and difference of binomials
15. Factor the sum and difference of cubes
16. Factor a perfect square trinomial as the square of a binomial
17. Factor a trinomial into two binomial factors
18. Factor binomials and trinomials completely

INEQUALITIES

19. Solve linear inequalities, including compound linear inequalities
20. Graph the solution set of a linear inequality
21. Use interval notation to describe the solution set of a linear inequality
22. Solve equations and inequalities involving absolute value
23. Solve linear inequalities in two variables and graph their solution sets

RATIONAL EXPRESSIONS

24. Define a rational expression
25. Find the values of the variable for which a rational expression is undefined
26. Write rational expressions in lowest terms
27. Multiply and divide rational expressions
28. Add and subtract rational expressions
29. Simplify a complex fraction involving rational expressions
30. Solve equations involving rational expressions
31. Solve applied problems using equations involving rational expressions

32. Find roots of real numbers
33. Decide whether a given root is rational, irrational, or not a real number
34. Use the Pythagorean Theorem
36. Convert between radical expressions and expressions using rational exponents