Factoring Flashcard Review

Front

What is factoring in algebra?

Back

Factoring is the process of breaking down an expression into a product of simpler expressions, or factors, that when multiplied together give the original expression.

Front

What is the greatest common factor (GCF)?

Back

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

Front

How do you factor a binomial expression?

Back

To factor a binomial, look for common factors or use special products like the difference of squares or sum/difference of cubes.

Front

What is a polynomial?

Back

A polynomial is an algebraic expression that consists of variables, coefficients, and non-negative integer exponents.

Front

What does it mean to factor completely?

Back

Factoring completely means breaking down an expression into its simplest factors, such that no further factoring is possible.

Front

What is the difference of squares?

Back

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

Front

How do you factor a trinomial of the form x² + bx + c?

Back

To factor a trinomial of this form, find two numbers that multiply to c and add to b, then express it as (x + m)(x + n) where m and n are those numbers.

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a trinomial that can be expressed as the square of a binomial, such as (a + b)² = a² + 2ab + b².

Front

How do you factor by grouping?

Back

To factor by grouping, group terms with common factors, factor out the GCF from each group, and then factor out the common binomial factor.

Front

What is the role of coefficients in factoring?

Back

Coefficients are the numerical factors in a polynomial. They can be factored out along with the variables when simplifying expressions.