Factoring Test Review

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 GCF (Greatest Common Factor)?

Back

The GCF is the largest factor that two or more numbers share. It is used to simplify expressions before factoring.

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 between factoring completely and factoring partially?

Back

Factoring completely means breaking down an expression into its simplest factors, while factoring partially means only factoring out some common factors or simplifying the expression to a certain extent.

Front

What is the factored form of x² + 7x - 30?

Back

(x + 10)(x - 3)

Front

How do you factor the expression 3x² + 18x + 15?

Back

First, factor out the GCF, which is 3, resulting in 3(x² + 6x + 5). Then, factor the quadratic to get 3(x + 5)(x + 1).

Front

What is the factored form of 4n² - 17n - 15?

Back

(n - 5)(4n + 3)

Front

How do you factor the expression 6x² + 5x - 6?

Back

To factor completely, find two numbers that multiply to -36 (6 * -6) and add to 5. The factored form is (3x - 2)(2x + 3).

Front

What does it mean to solve a quadratic equation?

Back

Solving a quadratic equation means finding the values of the variable that make the equation true, typically by finding the roots or x-intercepts.

Front

What is the factored form of n² + 5n - 6?

Back

(n + 6)(n - 1) or the roots are (1, 0) and (-6, 0).