Factoring Quadratics

Front

What is factoring in mathematics?

Back

Factoring is the process of breaking down an expression into a product of simpler expressions, called factors.

Front

What is a quadratic expression?

Back

A quadratic expression is a polynomial of degree 2, typically in the form ax² + bx + c, where a, b, and c are constants.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0.

Front

What does it mean for a quadratic to be factored?

Back

A quadratic is factored when it is expressed as the product of two binomials.

Front

What is the factored form of x² - 9?

Back

(x + 3)(x - 3) - This is an example of a difference of squares.

Front

What is the difference of squares?

Back

The difference of squares is a special factoring pattern that states a² - b² = (a + b)(a - b).

Front

How do you factor x² + 5x + 6?

Back

You can factor it as (x + 2)(x + 3).

Front

What is the zero-product property?

Back

The zero-product property states that if the product of two factors is zero, then at least one of the factors must be zero.

Front

What are the steps to factor a quadratic expression?

Back

1. Write the expression in standard form. 2. Identify a, b, and c. 3. Find two numbers that multiply to ac and add to b. 4. Rewrite the expression and factor by grouping.

Front

What is the factored form of 2x² + 8x?

Back

2x(x + 4) - This shows how to factor out the greatest common factor.