Factoring

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What does it mean to factor a polynomial?

Back

Factoring a polynomial means expressing it as a product of its factors, which are polynomials of lower degrees.

Front

What are the roots of a quadratic equation?

Back

The roots of a quadratic equation are the values of x that make the equation equal to zero.

Front

How do you find the roots of a quadratic equation using factoring?

Back

To find the roots using factoring, rewrite the quadratic in factored form (if possible) and set each factor equal to zero.

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 (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 involves rewriting a quadratic in the form (x - p)² = q to easily find its roots.

Front

What is a perfect square trinomial?

Back

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

Front

How do you factor a quadratic expression of the form x² + bx + c?

Back

To factor x² + bx + c, find two numbers that multiply to c and add to b, then express it as (x + m)(x + n), where m and n are those numbers.

Front

What is the difference of squares?

Back

The difference of squares is a special factoring case where a² - b² = (a - b)(a + b).