Simplifying Absolute Value Expressions
Simplify the expression: \( |5x^2 - 10x + 3| \)
Solving with Absolute Values
Solve the equation: \( |3x^2 - 2x - 1| = 2 \)
Rationalizing Radical Expressions
Rationalize the expression \(\frac{5}{\sqrt{2}}\).
Simplifying Radical Expressions
Simplify the expression \(\sqrt{50} + \sqrt{18}\)
Solving Radical Equations
Solve the radical equation: \(\sqrt{3x-2} = 2x + 1\).
Reducing
Reduce the following polynomial function: \(\frac{{3x^3 + 6x^2 - 9x - 18}}{{x^2 + 2x - 3}}\)
Cancelling the Common Factors
Simplify the rational function \(\frac{x^3 - x^2 - x + 1}{x^2 - 1}\)
Operations on Rational Expressions
Question 2 (20 Points)
Find the vertical and horizontal asymptotes then graph the following function:
\[
y=\frac{1}{x+3}-2
\]
Solving Rational Equations
Find the intercepts of the graph of the equation $y=\frac{x^{2}-4}{x^{2}-9}$
Quadratic Inequalities
Solve the quadratic inequality \(x^2 - 4x + 3 > 0\).
Rational Inequalities
Solve the rational inequality \(\frac{x^2 - 3x - 4}{x^2 - x - 2} > 0\).
Determining if the Expression is a Polynomial
Determine whether the expression \(5x^{2} + 3x^{-1} + 7\) is a polynomial.
Determining if Polynomial is Prime
Is the polynomial \(2x^2 + 3x - 2\) prime?
Determining if the Polynomial is a Perfect Square
Determine if the polynomial \(16x^4 - 24x^2 + 9\) is a perfect square.
Finding the Leading Term
Find the leading term of the polynomial function \(f(x) = 3x^5 - 4x^4 + 2x^3 - x + 5\)
Finding the Leading Coefficient
Given the function \(f(x) = 2x^3 - 5x^2 + 4x - 7\), find the leading coefficient.
Finding the Degree, Leading Term, and Leading Coefficient
Find the degree, leading term, and leading coefficient of the polynomial function \( P(x) = 4x^{5} - 3x^{4} + 2x^{3} - x^{2} + 5x - 6 \).