Solving for a Variable
Use the binomial theorem to find the term containing $x^{-33}$ in the expansion $\left(-3 x+\frac{1}{x^{9}}\right)^{7}$
Solving by Graphing
Given the equations \(y = 2x + 3\) and \(y = -x + 1\), find the point of intersection by graphing.
Polynomial Division
Divide the polynomial \(3x^3 - 2x^2 + 5x - 8\) by \(x - 2\).
Finding the Remainder Using Long Polynomial Division
Find the remainder when \(3x^{3}-4x^{2}+2x-5\) is divided by \(x-2\).
Synthetic Division
Use synthetic division to divide \(3x^3 - 2x^2 + 5x - 8\) by \(x - 2\).
Factoring Using Any Method
Factorize the following quadratic equation: \(x^2 - 5x + 6 = 0\)
Factoring a Difference of Squares
Factor the expression \(25x^2 - 9\)
Factoring a Sum of Cubes
Factor the expression \(x^3 + 8\)
Factoring Out Greatest Common Factor (GCF)
Factorize the expression \(15x^3y^2 - 10x^2y - 5xy\) by factoring out the Greatest Common Factor (GCF).
Factoring Trinomials
Factor the trinomial \(x^2 - 5x + 6\).
Partial Fraction Decomposition
Perform the partial fraction decomposition of the following rational function: \(\frac{3x^2-2x+1}{x^3-x^2}\).
Finding the Perfect Square Trinomial
Find the perfect square trinomial for the expression \(x^2 + 6x\)
Finding a Perpendicular Line Containing a Given Point
Find the equation of the line perpendicular to the line \(3x - 4y = 12\) and passes through the point \((2, -1)\).
Finding a Parallel Line Containing a Given Point
Find the equation of the line parallel to the line \(4x - 2y = 6\) and passing through the point \((1,2)\)
Reordering the Polynomial in Ascending Order
Reorder the polynomial \(7x^3 - 5x^2 + 9x - 4\) in ascending order.
Finding the LCM of a List of Expressions
Find the least common multiple (LCM) of the expressions \(15x^2y\), \(5xy^2\), and \(30x^3y^2\).
Finding the LCD of a List of Expressions
Find the Least Common Denominator (LCD) of the list of expressions: \(\frac{1}{x}, \frac{1}{x^2}, \frac{1}{x^3}\)
Determining if the Number is a Perfect Square
Determine whether the number 324 is a perfect square. If so, what is its square root?
Evaluate
Evaluate the expression \(5x^2 - 3x + 7\) when \(x = -2\).
Combining
Combine the expressions \(3x^2 - 5x + 7\) and \(4x^2 + 2x - 3\)
Finding the Domain
Find the domain of the function \(f(x) = \sqrt{2x+3}\)
Dividing
Divide the expression \(\frac{6x^2 - 5x - 1}{3x + 2}\) by \(2x - 1\).
Evaluate the Expression Using the Given Values
Evaluate the expression \(4x^2 - 3y + z\) for \(x = 2\), \(y = 1\), and \(z = 3\).
Evaluating the Difference Quotient
Evaluate the difference quotient for the function \(f(x) = 3x^2 + 2x + 1\).
Evaluating Radicals
Simplify the expression \(2\sqrt{8} + 3\sqrt{27}\).
Determining if True
If \( x = 2 \) and \( y = 3 \), is the equation \( 2x^2 - 3y + 5 = 7 \) true?
Finding the Holes in a Graph
Find the holes in the graph of the rational function \(f(x) = \frac{x^2 - 4}{x - 2}\).