Factor Completely

Front

What is factoring in mathematics?

Back

Factoring is the process of breaking down an expression into a product of simpler expressions, called factors.

Front

What does it mean to factor completely?

Back

To factor completely means to break down an expression into its simplest factors, such that no further factoring is possible.

Front

What is the greatest common factor (GCF)?

Back

The GCF is the largest factor that two or more numbers share. It is used to simplify expressions before factoring.

Front

How do you factor out the GCF from an expression?

Back

To factor out the GCF, divide each term of the expression by the GCF and write it outside the parentheses.

Front

Factor completely: 6m² + 16m

Back

2m(3m + 8)

Front

Factor completely: 3x⁵ - 27x³

Back

3x³(x - 3)(x + 3)

Front

What is a quadratic expression?

Back

A quadratic expression is a polynomial of degree 2, typically in the form ax² + bx + c.

Front

How do you factor a quadratic expression?

Back

To factor a quadratic expression, find two numbers that multiply to ac (the product of a and c) and add to b.

Front

Factor completely: 3x² + 18x + 15

Back

3(x + 5)(x + 1)

Front

What is the difference of squares?

Back

The difference of squares is a special factoring pattern: a² - b² = (a - b)(a + b).