Factoring

Front

What is factoring in algebra?

Back

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

Front

What is a quadratic expression?

Back

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

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 standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants.

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 perfect square trinomial?

Back

A perfect square trinomial can be factored as (a + b)² or (a - b)², where a² + 2ab + b² = (a + b)² and a² - 2ab + b² = (a - b)².

Front

What is the first step in factoring a quadratic expression?

Back

The first step is to look for a common factor in all terms of the expression.

Front

How do you factor the expression x² + 16x + 64?

Back

The expression factors to (x + 8)(x + 8), which is a perfect square trinomial.

Front

What is the factored form of 2x² + 22x + 60?

Back

The factored form is 2(x + 5)(x + 6).

Front

What is the factored form of 3x² + 5x - 12?

Back

The factored form is (3x - 4)(x + 3).