Factoring

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 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 and a ≠ 0.

Front

What is the first step in factoring a polynomial?

Back

The first step in factoring a polynomial is to look for the greatest common factor (GCF) of the terms.

Front

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

Back

To factor a quadratic expression of the form x² + bx + c, find two numbers that multiply to c and add to b, then express the quadratic as (x + m)(x + n), where m and n are those two numbers.

Front

What is the difference of squares formula?

Back

The difference of squares formula states that a² - b² = (a + b)(a - b).

Front

How do you factor a trinomial of the form ax² + bx + c?

Back

To factor a trinomial of the form ax² + bx + c, look for two numbers that multiply to ac and add to b, then rewrite the middle term and factor by grouping.

Front

What is the significance of the leading coefficient in factoring?

Back

The leading coefficient (the coefficient of the highest degree term) affects the methods used for factoring, especially in trinomials.

Front

What is the process of factoring by grouping?

Back

Factoring by grouping involves rearranging and grouping terms in a polynomial to factor out common factors from each group.

Front

What does it mean to factor completely?

Back

To factor completely means to break down an expression into its simplest factors, including all prime factors and GCF.

Front

What is a perfect square trinomial?

Back

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