Solving Quadratic Equations by Factoring

Front

What is a quadratic equation?

Back

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

Front

What does it mean to factor a quadratic equation?

Back

Factoring a quadratic equation means expressing it as a product of two binomials, such as (x - p)(x - q) = 0, where p and q are the solutions.

Front

What are the solutions of the quadratic equation x² + 5x + 6 = 0?

Back

x = -3 or x = -2.

Front

What are the solutions of the quadratic equation x² + 2x - 15 = 0?

Back

x = -5 or x = 3.

Front

What are the solutions of the quadratic equation x² + 12x + 35 = 0?

Back

x = -5 or x = -7.

Front

What are the solutions of the quadratic equation x² - 6x + 8 = 0?

Back

x = 2 or x = 4.

Front

What are the solutions of the quadratic equation x² + x + 3 = 0?

Back

No solutions.

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

How do you determine the number of solutions for a quadratic equation?

Back

The number of solutions can be determined using the discriminant (b² - 4ac). If it's positive, there are two solutions; if zero, one solution; if negative, no real solutions.

Front

What is the discriminant of a quadratic equation?

Back

The discriminant is the expression b² - 4ac in the quadratic formula, which helps determine the nature and number of solutions.