Factoring Basics

Front

What is factoring in mathematics?

Back

Factoring is the process of breaking down an expression into a product of simpler factors that, when multiplied together, give the original expression.

Front

What is the greatest common factor (GCF)?

Back

The greatest common factor (GCF) 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 and divide each term by this factor, then write the expression as the GCF multiplied by the remaining terms.

Front

What are the steps to factor a quadratic expression of the form ax^2 + 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 a zero of a polynomial?

Back

A zero of a polynomial is a value of x that makes the polynomial equal to zero.

Front

How do you find the zeros of a quadratic equation?

Back

You can find the zeros of a quadratic equation by factoring, using the quadratic formula, or completing the square.

Front

What is the difference between factoring and expanding an expression?

Back

Factoring is breaking down an expression into simpler components, while expanding is multiplying out the components to form a single expression.

Front

What is the factored form of x^2 - 5x + 6?

Back

(x - 2)(x - 3) because -2 and -3 multiply to 6 and add to -5.

Front

What are the two numbers that multiply to -15 and add up to -2?

Back

-5 and 3.

Front

What are the two numbers that multiply to 8 and add up to 9?

Back

1 and 8.