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 is the largest factor that divides two or more numbers or 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 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 x² + bx + c?

Back

To factor a trinomial of this form, find two numbers that multiply to c and add to b, then rewrite the expression as (x + m)(x + n), where m and n are the two numbers.

Front

What is the factored form of x² - 25?

Back

The factored form of x² - 25 is (x + 5)(x - 5), which is an example of the difference of squares.

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, divide each term by the GCF, and express the original expression as the product of the GCF and the resulting expression.

Front

What is the factored form of 3x² + 18x + 15?

Back

The factored form is 3(x + 5)(x + 1).

Front

How do you factor a quadratic expression when a is not equal to 1?

Back

When a is not equal to 1, use the method of grouping or the AC method, where you multiply a and c, find two numbers that multiply to that product and add to b, and then factor by grouping.

Front

What is the factored form of x² - 5x - 14?

Back

The factored form is (x + 2)(x - 7).