Factoring and Solving by 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 Greatest Common Factor (GCF)?

Back

The GCF of two or more terms is the largest expression that divides each of the terms without leaving a remainder.

Front

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

Back

To factor a quadratic expression, look for two numbers that multiply to ac (the product of a and c) and add to b. Rewrite the expression using these numbers to factor by grouping.

Front

What is the factored form of a quadratic expression?

Back

The factored form of a quadratic expression is expressed as (px + q)(rx + s), where p, q, r, and s are constants.

Front

What is the process of factoring by grouping?

Back

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

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 the trinomial as (x + m)(x + n), where m and n are the two numbers.

Front

What is the difference of squares formula?

Back

The difference of squares formula states that a² - b² = (a + b)(a - b). This is used to factor expressions that are the difference of two perfect squares.

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is an expression of the form a² ± 2ab + b², which can be factored as (a ± b)².

Front

How do you factor a polynomial completely?

Back

To factor a polynomial completely, first factor out the GCF, then apply techniques such as grouping, difference of squares, or recognizing special products until no further factoring is possible.

Front

What is the role of the leading coefficient in factoring quadratics?

Back

The leading coefficient (the coefficient of x²) affects the methods used for factoring; if it is not 1, additional steps may be needed to factor the quadratic.