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 does GCF stand for in factoring?

Back

GCF stands for Greatest Common Factor, which is the largest factor that divides two or more numbers.

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 write the expression as the product of the GCF and the resulting expression.

Front

What is the factored form of a quadratic expression?

Back

The factored form of a quadratic expression is typically written as (x - p)(x - q), where p and q are the roots of the quadratic equation.

Front

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

Back

1. Identify a, b, and c. 2. Find two numbers that multiply to a*c and add to b. 3. Rewrite the middle term using these two numbers. 4. Factor by grouping.

Front

What is the difference between factoring and expanding an expression?

Back

Factoring is breaking down an expression into its factors, while expanding is multiplying out the factors to get back to the original expression.

Front

What is the factored form of the expression 3n² - 15n + 18?

Back

3(n - 3)(n - 2) is the factored form of the expression 3n² - 15n + 18.

Front

How do you factor the expression x² + 7x - 30?

Back

To factor x² + 7x - 30, find two numbers that multiply to -30 and add to 7, which are 10 and -3. Thus, it factors to (x + 10)(x - 3).

Front

What are the steps to factor a trinomial of the form a² + bx + c?

Back

1. Identify a, b, and c. 2. Find two numbers that multiply to a*c and add to b. 3. Rewrite the expression using these numbers. 4. Factor by grouping.

Front

What is the factored form of a² - a - 12?

Back

The factored form of a² - a - 12 is (a - 4)(a + 3).