Factoring Binomials and Trinomials

Front

What is factoring in algebra?

Back

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

Front

What is a binomial?

Back

A binomial is a polynomial that contains exactly two terms, such as (x + 5) or (3y - 2).

Front

What is a trinomial?

Back

A trinomial is a polynomial that contains exactly three terms, such as (x^2 + 5x + 6) or (2y^2 - 3y + 1).

Front

What does it mean to fully factor an expression?

Back

To fully factor an expression means to break it down into its simplest factors, which cannot be factored further.

Front

What is the difference of squares?

Back

The difference of squares is a special factoring pattern that applies to expressions of the form a^2 - b^2, which can be factored as (a - b)(a + b).

Front

Factor the expression: 4x^2 - 121

Back

(2x - 11)(2x + 11) - This is an example of the difference of squares.

Front

How do you factor a common factor out of an expression?

Back

To factor out a common factor, identify the greatest common factor (GCF) of the terms and divide each term by the GCF, then write it outside the parentheses.

Front

Factor the expression: -21x + 35

Back

7(-3x + 5) - Here, 7 is the common factor.

Front

What is the process for factoring trinomials?

Back

To factor trinomials, look for two numbers that multiply to the constant term and add to the coefficient of the middle term.

Front

Factor the expression: x^2 + 9x - 36

Back

(x + 12)(x - 3) - The numbers 12 and -3 multiply to -36 and add to 9.