Solving Quadratic Equations by Factoring

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

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. This is used to solve equations of the form (x - p)(x - q) = 0.

Front

How do you factor a quadratic equation?

Back

To factor a quadratic equation, you need to express it in the form (x - p)(x - q) = 0, where p and q are the solutions of the equation.

Front

What is the first step in solving 3x² - 3x - 36 = 0?

Back

Factor out 3 first (GCF), and then divide both sides by 3.

Front

What are the solutions to (x + 9)(x + 6) = 0?

Back

x = -9, -6.

Front

Solve x² + 2x - 20 = 4 by rearranging it to standard form.

Back

x² + 2x - 24 = 0.

Front

What are the solutions to (x - 3)(x + 2) = 0?

Back

x = 3, -2.

Front

What does it mean to solve by factoring?

Back

Solving by factoring means rewriting the equation as a product of its factors and then using the zero product property to find the solutions.

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 significance of the coefficients a, b, and c in a quadratic equation?

Back

The coefficient 'a' determines the direction of the parabola (upward or downward), 'b' affects the position of the vertex, and 'c' is the y-intercept.