Factoring and GCF Flashcard

Front

What is the Greatest Common Factor (GCF)?

Back

The GCF is the largest positive integer that divides all the given numbers without leaving a remainder.

Front

How do you factor out the GCF from an expression?

Back

To factor out the GCF, identify the largest factor common to all terms in the expression, then divide each term by the GCF and write the expression as the GCF multiplied by the resulting expression.

Front

What is the factored form of a quadratic expression?

Back

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

Front

What is the process to factor a trinomial of the form ax² + bx + c?

Back

To factor a trinomial, find two numbers that multiply to ac (the product of a and c) and add to b. Rewrite the middle term using these numbers, then factor by grouping.

Front

What does it mean to factor completely?

Back

Factoring completely means breaking down an expression into its simplest factors, including any GCF and irreducible factors.

Front

How do you solve a quadratic equation by factoring?

Back

To solve a quadratic equation by factoring, first set the equation to zero, factor the quadratic expression, then set each factor equal to zero and solve for the variable.

Front

What is the significance of setting an equation equal to zero when solving for x?

Back

Setting an equation equal to zero allows you to apply the Zero Product Property, which states that if the product of two factors is zero, at least one of the factors must be zero.

Front

What is the Zero Product Property?

Back

The Zero Product Property states that if ab = 0, then either a = 0 or b = 0.

Front

How do you factor a binomial expression?

Back

To factor a binomial, look for common factors or apply special factoring formulas such as the difference of squares or the sum/difference of cubes.

Front

What is the difference of squares formula?

Back

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