Polynomial and Rational Functions

Simplifying Absolute Value Expressions

Simplify the expression:

| 5 x^{2} - 10 x + 3 |

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Solving with Absolute Values

Solve the equation:

| 3 x^{2} - 2 x - 1 | = 2

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Rationalizing Radical Expressions

Rationalize the expression

\frac{5}{\sqrt{2}}

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Simplifying Radical Expressions

Simplify the expression

\sqrt{50} + \sqrt{18}

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Solving Radical Equations

Solve the radical equation:

\sqrt{3 x - 2} = 2 x + 1

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Reducing

Reduce the following polynomial function:

\frac{3 x^{3} + 6 x^{2} - 9 x - 18}{x^{2} + 2 x - 3}

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Cancelling the Common Factors

Simplify the rational function

\frac{x^{3} - x^{2} - x + 1}{x^{2} - 1}

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Operations on Rational Expressions

Question 2 (20 Points) Find the vertical and horizontal asymptotes then graph the following function:

y = \frac{1}{x + 3} - 2

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Solving Rational Equations

Find the intercepts of the graph of the equation

y = \frac{x^{2} - 4}{x^{2} - 9}

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Quadratic Inequalities

Solve the quadratic inequality

x^{2} - 4 x + 3 > 0

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Rational Inequalities

Solve the rational inequality

\frac{x^{2} - 3 x - 4}{x^{2} - x - 2} > 0

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Determining if the Expression is a Polynomial

Determine whether the expression

5 x^{2} + 3 x^{- 1} + 7

is a polynomial.

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Determining if Polynomial is Prime

Is the polynomial

2 x^{2} + 3 x - 2

prime?

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Determining if the Polynomial is a Perfect Square

Determine if the polynomial

16 x^{4} - 24 x^{2} + 9

is a perfect square.

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Finding the Leading Term

Find the leading term of the polynomial function

f (x) = 3 x^{5} - 4 x^{4} + 2 x^{3} - x + 5

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Finding the Leading Coefficient

Given the function

f (x) = 2 x^{3} - 5 x^{2} + 4 x - 7

, find the leading coefficient.

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Finding the Degree, Leading Term, and Leading Coefficient

Find the degree, leading term, and leading coefficient of the polynomial function

P (x) = 4 x^{5} - 3 x^{4} + 2 x^{3} - x^{2} + 5 x - 6

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Simplifying Absolute Value Expressions

Solving with Absolute Values

Rationalizing Radical Expressions

Simplifying Radical Expressions

Solving Radical Equations

Reducing

Cancelling the Common Factors

Operations on Rational Expressions

Solving Rational Equations

Quadratic Inequalities

Rational Inequalities

Determining if the Expression is a Polynomial

Determining if Polynomial is Prime

Determining if the Polynomial is a Perfect Square

Finding the Leading Term

Finding the Leading Coefficient

Finding the Degree, Leading Term, and Leading Coefficient

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