Factoring Quadratic Expressions

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 and a ≠ 0.

Front

What does it mean to factor a quadratic expression?

Back

Factoring a quadratic expression involves rewriting it as a product of two binomials, such as (px + q)(rx + s), where p, q, r, and s 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 is the relationship between the roots of a quadratic equation and its factors?

Back

The roots of a quadratic equation are the values of x that make the equation equal to zero, and they correspond to the values that make each factor equal to zero.

Front

How can you determine the factors of a quadratic expression?

Back

To determine the factors, look for two numbers that multiply to give the constant term (c) and add to give the coefficient of the linear term (b).

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant, given by b² - 4ac, determines the nature of the roots: if positive, there are two distinct real roots; if zero, one real root; if negative, two complex roots.

Front

What is the process of completing the square?

Back

Completing the square is a method used to convert a quadratic expression into a perfect square trinomial, which can then be factored easily.

Front

What are the steps to factor a quadratic expression by grouping?

Back

1. Rewrite the quadratic in standard form. 2. Find two numbers that multiply to ac and add to b. 3. Split the middle term using these numbers. 4. Factor by grouping.

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a quadratic expression that can be expressed as the square of a binomial, such as (a + b)² = a² + 2ab + b².