Algebraic Operations

Factoring polynomials of the form a^2 + 2ab + b^2 or a^2 - 2ab + b^2

- If the sign in front of the 2ab term is positive, the polynomial is equal to (a + b)^2 - If the sign in front of the 2ab term is negative, the polynomial is equal to (a - b)^2

Factoring the product of binomials

- The polynomial can be factored into the two binomials, each containing an x term - The product of the two missing terms will be the last term in the polynomial - The sum of the two missing terms will be the coefficient of the second term of the polynomial

Inequalities

- The solution to an inequality is almost always a range of values rather than a single value - Multiplication or division by a negative number causes the reversal of the direction of inequality sign

Solving equations

Always perform the same operation on both sides of the equal sign

Quadratic equations

An equation of the form: f(x) = ax² + bx + c = 0, a≠0. Able to be solved by factoring the algebraic expression, setting each of the factors equal to zero, and solving the resulting equations.

Factoring the difference of squares

Any polynomial of the form a^2 - b^2 can be factred into the form (a - b)(a + b).

Using Picking Numbers to solve for one unknown in terms of another

If the first number picked doesn't lead to a single correct answer: - Either pick a new number - or Guess strategically among the answers which haven't been eliminated

Solving for one unknown in terms of another

Isolate the desired variable on one side of the equation and move all the constants and other variables to the other side

Sequence

Lists of numbers or formulas that define each element

Picking Numbers Strategy

Picking a number for variable themed or algebraic expression problem to make the problem less abstract. Helps to evaluate the answer choices and the information in the question stem by picking a number and substituting it for the variable wherever the variable appears.

Factoring algebraic expressions

Reformatting an expression as a product of two or more simpler expressions. Common factors can be factored out by using the distributive law.

Backsolving Strategy

Substituting each answer choice from a multiple choice question into the equation until one satisfies the equation

Substitution

The process of replacing a variable in an expression with another value, used to evaluate an algebraic expression or to express it in terms of other variables.

Combining like terms

The process of simplifying an expression by adding together or subtracting terms that have the same variable factors.

FOIL method

To multiply two binomials, find the sum of the products of the First terms, the Outer terms, the Inner terms, and the Last terms