Factoring Completely

Front

What is factoring completely?

Back

Factoring completely is the process of breaking down an expression into its simplest factors, such that when multiplied together, they yield the original expression.

Front

What is the greatest common factor (GCF)?

Back

The greatest common factor (GCF) is the largest factor that divides two or more numbers or expressions without leaving a remainder.

Front

How do you factor out the GCF from an expression?

Back

To factor out the GCF, identify the largest factor common to all terms in the expression, then divide each term by the GCF and write the expression as the GCF multiplied by the resulting expression.

Front

What is a quadratic expression?

Back

A quadratic expression is a polynomial of degree 2, typically in the form ax² + bx + c, where a, b, and c are constants.

Front

What does it mean for an expression to be prime?

Back

An expression is considered prime if it cannot be factored into simpler expressions with integer coefficients.

Front

How do you factor a quadratic expression?

Back

To factor a quadratic expression, look for two numbers that multiply to give ac (the product of a and c) and add to give b (the coefficient of x). Use these numbers to rewrite the expression.

Front

What is the difference of squares?

Back

The difference of squares is a special factoring pattern that applies to expressions of the form a² - b², which can be factored as (a + b)(a - b).

Front

What is the sum of cubes?

Back

The sum of cubes is a factoring pattern for expressions of the form a³ + b³, which can be factored as (a + b)(a² - ab + b²).

Front

What is the product of cubes?

Back

The product of cubes is a factoring pattern for expressions of the form a³ - b³, which can be factored as (a - b)(a² + ab + b²).

Front

How do you factor a trinomial?

Back

To factor a trinomial, find two binomials that multiply to give the original trinomial. This often involves finding two numbers that multiply to the constant term and add to the linear coefficient.