INTERMEDIATE ALGEBRA
Chapter 4 POLYNOMIALS AND POLYNOMIAL FUNCTIONS Section:
4.1 – 4.8
Outcomes:
Upon completion of this unit students will be able to perform standard
polynomial operations and
solve equations involving polynomials.
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F |
N |
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Specific Competencies
Demonstrate the ability to: |
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4.1 |
Define monomial and determine the coefficient and
degree of a monomial. |
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4.1 |
Define polynomial and determine the degree of a
polynomial. |
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4.1 |
Simplify polynomials by combining like terms. |
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4.1 |
Evaluate polynomial functions. |
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4.1 |
Add and subtract polynomial functions. |
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4.2 |
Multiply a monomial and a polynomial. |
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4.2 |
Multiply a binomial by a binomial. |
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4.2 |
Multiply a polynomial by a polynomial. |
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4.2 |
Multiply a polynomial by a polynomial. |
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4.2 |
Multiply polynomial functions. |
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4.3 |
Divide a polynomial by a monomial. |
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4.3 |
Divide polynomials using long division. |
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4.3 |
Divide polynomials using synthetic division. |
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4.3 |
Divide polynomial functions. |
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4.3 |
Use the remainder and factor theorems. |
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4.4 |
Factor the greatest common factor. |
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4.4 |
Factor by grouping. |
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4.5 |
Factor trinomials of the form x2 +
bx + c. |
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4.5 |
Factor trinomials of the form ax2 +
bx + c. |
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4.5 |
Factor trinomials using substitution. |
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4.6 |
Factor perfect square trinomials. |
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4.6 |
Factor the difference of two squares. |
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4.6 |
Factor the sum or difference of two cubes. |
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4.7 |
Factor polynomials completely. |
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4.7 |
Write polynomial functions in factored form. |
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4.8 |
Solve polynomial equations using the
zero-product property. |
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4.8 |
Solve equations involving polynomial functions. |
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4.8 |
Model and solve problems involving polynomials. |
Chapter 5 RATIONAL EXPRESSIONS AND RATIONAL FUNCTIONS
Section: 5.1 – 5.6
Outcomes: Upon completion of this unit students will be able to solve equations
involving rational expressions.
| A |
B |
C |
D |
F |
N |
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Specific Competencies
Demonstrate the ability to: |
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5.1 |
Determine the domain of a rational expression. |
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5.1 |
Simplify rational expressions. |
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5.1 |
Multiply rational expressions. |
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5.1 |
Divide rational expressions. |
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5.1 |
Work with rational functions. |
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5.2 |
Add or subtract rational expressions with a
common denominator. |
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5.2 |
Find the least common denominator of two or more
rational expressions. |
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5.2 |
Add or subtract rational expressions with
different denominators. |
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5.3 |
Simplify a complex rational expression by
simplifying the numerator and denominator
separately |
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5.3 |
Simplify a complex rational expression using the
least common denominator. |
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5.4 |
Solve equations containing rational
expressions. |
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5.4 |
Solve equations involving rational functions. |
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*5.5 |
Solve a rational inequality. |
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5.6 |
Solve for a variable in a rational expression. |
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5.6 |
Model and solve ratio and proportion problems. |
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5.6 |
Model and solve work problems. |
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5.6 |
Model and solve uniform motion problems. |
Chapter 6 RADICALS AND RATIONAL EXPONENTS Section: 6.1
– 6.8
Outcomes:
Upon completion of this unit students will be able to simplify expressions
containing rational
exponents and radicals and solve equations containing such expressions.
| A |
B |
C |
D |
F |
N |
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Specific Competencies
Demonstrate the ability to: |
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6.1 |
Evaluate nth roots. |
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6.1 |
Simplify expressions that are in radical form. |
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6.1 |
Evaluate expressions of the form a1/n. |
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6.1 |
Evaluate expressions of the form am/n. |
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6.2 |
Use the laws of exponents to simplify expressions
involving rational
exponents. |
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6.2 |
Use the laws of exponents to simplify radical
expressions |
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6.2 |
Factor expressions containing rational exponents. |
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6.3 |
Use the product property to multiply radical
expressions. |
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6.3 |
Use the product property to simplify radical
expressions. |
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6.3 |
Use the quotient property to simplify radical
expressions. |
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6.3 |
Multiply radicals with unlike indices. |
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6.4 |
Add or subtract radical expressions. |
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6.4 |
Multiply radical expressions. |
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6.5 |
Rationalize a denominator containing one term. |
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6.5 |
Rationalize a denominator containing two
terms. |
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6.6 |
Evaluate functions whose rule is a radical
expression. |
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6.6 |
Find the domain of a function whose rule contains
a radical. |
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6.6 |
Graph functions involving square roots. |
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6.6 |
Graph functions involving cube roots. |
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6.7 |
Solve radical equations containing one
radical. |
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6.7 |
Solve radical equations containing two
radicals. |
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*6.7 |
Solve for a variable in a radical equation. |
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6.8 |
Evaluate the square root of negative real
numbers. |
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6.8 |
Add or subtract complex numbers. |
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6.8 |
Multiply complex numbers. |
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6.8 |
Divide complex numbers. |
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6.8 |
Evaluate the powers of i. |
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