Algebra concepts, explained
- How do you find the zeros of a polynomial?
Learn how to find the zeros of a polynomial by setting the equation to zero, factoring, and solving for x, with step-by-step examples.
- What is the Remainder Theorem and How Do You Use It?
Learn what the remainder theorem is, how it connects polynomial division to evaluating functions, and how to use it to solve algebra problems quickly.
- How do you divide polynomials with long division?
Learn how to divide polynomials using long division, a method similar to dividing regular numbers, complete with steps, examples, and common mistakes.
- How do you graph a system of linear inequalities?
Learn how to graph systems of linear inequalities by graphing each line, shading the correct regions, and finding where the shaded areas overlap.
- Why does the inequality sign flip when you multiply by a negative?
Learn why multiplying or dividing an inequality by a negative number forces the inequality sign to flip, using number lines and everyday analogies.
- How do you solve an absolute value inequality?
Learn how to solve absolute value inequalities by converting them into compound inequalities, with clear step-by-step examples and common pitfalls.
- How do you solve a system with three variables?
Learn how to solve a system of three linear equations with three variables by systematically eliminating one variable at a time.
- When should you use substitution versus elimination?
Learn how to choose between substitution and elimination when solving systems of equations by looking at the coefficients of your variables.
- What does it mean when a system has no solution or infinitely many?
Learn what it means algebraically and graphically when a system of linear equations has no solution (parallel lines) or infinitely many solutions (the same line).
- How do you solve an equation where the variable is in the exponent?
Learn how to solve exponential equations by using logarithms to bring the variable down from the exponent, with step-by-step examples and common mistakes.
- What is a logarithm, really?
A logarithm is simply an exponent in reverse, telling you what power a base must be raised to in order to reach a specific number.
- Why is anything to the power of zero equal to one?
Understand why any non-zero number raised to the power of zero equals one by looking at the rules of exponents and a simple dividing pattern.
- How do negative exponents work?
A negative exponent tells you to divide instead of multiply. To evaluate a negative exponent, take the reciprocal of the base and make the exponent positive.
- How do you tell if a function is one-to-one?
Learn how to determine if a function is one-to-one using the horizontal line test and algebraic methods, with easy examples and standard definitions.
- How do you factor a quadratic when the leading coefficient is not 1?
Learn how to factor quadratic expressions where the leading coefficient is not 1 using the ac method and factoring by grouping.
- What does f(x) actually mean?
Understand what f(x) means in algebra, how function notation works like a machine, and why it replaces "y" in math equations.
- What is the difference between a relation and a function?
Learn the key difference between relations and functions in algebra, including how to identify them using mappings and the vertical line test.
- How do you find the domain and range of a function?
Learn how to find the domain and range of a function, including how to spot restrictions like dividing by zero, with clear examples and everyday analogies.
- How Do You Complete the Square, and Why Does It Work?
Learn how to complete the square to solve quadratic equations, why the method works visually, and how to avoid common algebraic mistakes.
- What does the discriminant tell you?
The discriminant tells you the number and type of solutions to a quadratic equation without having to solve the entire formula.
- How do you know which method to use to solve a quadratic equation?
Learn how to choose between factoring, taking square roots, completing the square, and the quadratic formula to solve any quadratic equation.
- What does it mean to isolate the variable?
Isolating the variable means getting the letter by itself on one side of an equation to find its value.
- How do you solve an equation with fractions in it?
Learn how to easily solve linear equations with fractions by finding a common denominator to clear the fractions and simplify your math.
- Why can you do the same thing to both sides of an equation?
You can do the same thing to both sides of an equation because applying identical operations preserves the underlying balance and equality.