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 factored form of a quadratic expression?

Back

The factored form of a quadratic expression is typically written as (ax + b)(cx + d), where a, b, c, and d are constants.

Front

How do you factor a quadratic expression of the form ax^2 + bx + c?

Back

To factor a quadratic expression of the form ax^2 + bx + c, look for two numbers that multiply to ac (the product of a and c) and add to b. Then, rewrite the expression using these numbers to group and factor.

Front

What is the difference of squares formula?

Back

The difference of squares formula states that a^2 - b^2 = (a + b)(a - b).

Front

What is the sum of squares formula?

Back

The sum of squares cannot be factored over the real numbers, but it can be expressed as a product of complex numbers: a^2 + b^2 = (a + bi)(a - bi).

Front

What is a common factor?

Back

A common factor is a number or expression that divides two or more numbers or expressions without leaving a remainder.

Front

How do you factor by grouping?

Back

To factor by grouping, divide the expression into groups, factor out the common factor from each group, and then factor out the common binomial factor.

Front

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

Back

The leading coefficient (the coefficient of the x^2 term) affects the methods used for factoring; if it is 1, simpler methods can be used, while if it is greater than 1, additional steps may be needed.

Front

What is the zero-product property?

Back

The zero-product property states that if the product of two factors is zero, then at least one of the factors must be zero.

Front

How do you check if your factors are correct?

Back

To check if your factors are correct, multiply the factors back together to see if you obtain the original expression.