## MTH 9 - Bundle 6-9 - Exponents, Factoring, Poly Equations, Rational Expressions and ... at Lord Fairfax Community College

### Course Description

Effective: 2017-08-01

Includes performing operations on exponential expressions and polynomials, factoring polynomials, solving polynomial equations, simplifying rational algebraic expressions, solving rational algebraic equations, simplifying radical expressions, using rational exponents, solving radical equations, working with functions in different forms: ordered pair, graph, and equation form. Also introduces quadratic functions, their properties and their graphs. Emphasis should be on learning all the different factoring methods, and solving application problems using polynomial, rational and radical equations. Credit is not applicable toward graduation.

Lecture 4 hours. Total 4 hours per week.

4 credits

### General Course Purpose

To prepare students for successful entry into credit mathematics courses as well as other credit courses requiring basic math competencies as prerequisites.

### Course Prerequisites/Corequisites

Prerequisites: MTE 1-5 or qualifying placement score.

### Course Objectives

- Exponents
- Evaluate the product of two exponential expressions.
- Evaluate the quotient of two exponential expressions.
- Evaluate the power of a power of an exponential expression.
- Evaluate exponential expressions that contain combinations of products, quotients, power of a power and negative exponents.
- Polynomials
- Identify an expression as a monomial, binomial, trinomial or polynomial.
- Add and subtract monomials using the rules of exponents.
- Add and subtract binomials.
- Add and subtract trinomials.
- Multiply monomials using the rules of exponents.
- Multiply combinations of binomials and trinomials.
- Evaluate exponential expressions that contain negative exponents.
- Multiply and divide numbers in Scientific Notation.
- Divide polynomials.
- Factoring
- Find the greatest common factor from a list of terms.
- Find the greatest common factor from a polynomial.
- Factor a polynomial by grouping.
- Factor trinomials of the form x2 + bx + c.
- Factor trinomials of the form ax2 + bx + c, trials and ac method.
- Factor a difference of squares.
- Factor a sum of two cubes.
- Factor a difference of two cubes.
- Solve equations using factoring techniques.
- Solve application problems involving polynomial equations and factoring.
- Rational Expressions and Equations
- Identify the real value of the variable for which a rational algebraic expression having a denominator of the form ax + b is undefined.
- Identify all real values of the variable for which a rational algebraic expression having a denominator of the form ax2 + bx + c is undefined.
- Simplify a rational algebraic expression.
- Evaluate a rational algebraic expression given specific integral values for each variable.
- Perform multiplication of rational algebraic expressions and express the product in simplest terms.
- Use factorization to divide rational algebraic expressions and express the quotient in simplest terms.
- Divide a polynomial by a monomial.
- Perform polynomial long division.
- Find the Least Common Denominator (LCD) of two or more rational algebraic expressions.
- Perform addition and subtraction of rational algebraic expressions having like denominators.
- Perform addition and subtraction of rational algebraic expressions having denominators that have no common factors.
- Perform addition and subtraction of rational algebraic expressions having denominators that have a common monomial factor.
- Perform addition and subtraction of rational algebraic expressions having denominators that have a common binomial factor.
- Simplify complex fractions.
- Solve rational algebraic equations.
- Write a rational equation to match the information given in an application problem.
- Solve an application problem using rational equations.
- Radical Expressions and Rational Exponents
- Convert between square root and a1/2 forms.
- Simplify square roots.
- Simplify nth roots of variable expressions.
- Compute and estimate radicals.
- Calculate square roots via calculator.
- Estimate square roots.
- Calculate nth roots via calculator.
- Simplify using the properties of rational exponents.
- Simplify radicals by using the multiplication property of radicals.
- Simplify radicals by using the division property of radicals.
- Convert between nth root and a1/n forms.
- Convert between combinations of nth root and mth power and am/n forms.
- Define like radicals.
- Combine and simplify like radicals.
- Multiply and simplify radicals.
- Rationalize the denominator (one term and two terms).
- Simplify radicals by rationalizing a denominator with one term.
- Simplify radicals by rationalizing a denominator with two terms.
- Solve radical equations.
- Solve application problems involving radicals.
- Solve problems involving right triangles.
- Solve problems involving the Pythagorean Theorem.
- Solve problems involving the distance formula.
- Define the imaginary unit i and imaginary numbers.
- Simplify square roots of negative numbers using the imaginary unit.
- Functions
- Determine if a relation is a function and identify the domain and range of the function.
- Determine if a list of ordered pairs, graph, or equation is a function.
- Determine the domain and range of a function given as a list of ordered pairs.
- Determine the domain and range of a function given as a graph.
- Determine the domain of a function given as an equation.
- Evaluate for constant values of and for specific monomials and binomials.
- Quadratics
- Find all roots of quadratic equations using both the square root method and the quadratic formula.
- Find the roots of quadratic equations of the form.
- Find the roots of quadratic equations of the form when the discriminant is a positive perfect square, (i.e. the quadratic is factorable).
- Find the roots of quadratic equations of the form when the discriminant is positive, but not a perfect square.
- Find the roots of quadratic equations of the form when the discriminant is zero.
- Find the roots of quadratic equations of the form when the discriminant is negative.
- Describe the roots of a quadratic based upon the discriminant in all cases.
- Analyze a quadratic function to determine its vertex by completing the square and using the formula.
- Write a quadratic function in vertex form by completing the square for quadratics with and identify the vertex.
- Find the vertex of a quadratic equation using the formula method.
- Graph a quadratic function, using the vertex form, indicating the intercepts and vertex.
- Determine whether the parabola opens upward or downward.
- Plot the vertex of the parabola.
- Determine the axis of symmetry for the parabola.
- Plot the -intercepts of the parabola, if they exist.
- Plot the -intercept of the parabola and complete the graph with additional points as needed.
- Apply knowledge of quadratic functions to solve application problems from geometry, economics, applied physics, and other disciplines.
- Solve problems involving area optimization.
- Solve problems involving revenue optimization.
- Solve problems involving the motion of falling objects.

### Major Topics to be Included

- Exponents, Factoring, and Polynomial Equations
- Rational Expressions and Equations
- Rational Exponents and Radicals
- Functions, Quadratic Equations, and Parabolas