Solving quadratics 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 does it mean to factor a quadratic equation?

Back

Factoring a quadratic equation involves rewriting it as a product of two binomial expressions, such as (x - p)(x - q) = 0, where p and q are the roots of the equation.

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 solve (x - 3)(x + 6) = 0?

Back

Set each factor equal to zero: x - 3 = 0 or x + 6 = 0. This gives x = 3 or x = -6.

Front

What are the roots of the equation x² + 9x + 20 = 0?

Back

The roots are x = -4 and x = -5, found by factoring the equation as (x + 4)(x + 5) = 0.

Front

What is the first step in solving (x + 2)(x - 3) = 0?

Back

The first step is to set each binomial factor equal to zero: x + 2 = 0 or x - 3 = 0.

Front

How do you factor x² - 9?

Back

x² - 9 can be factored as (x - 3)(x + 3) using the difference of squares.

Front

What are the solutions to x² - 9x + 20 = 0?

Back

The solutions are x = 4 and x = 5, found by factoring the equation as (x - 4)(x - 5) = 0.

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.

Front

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

Back

The coefficients a, b, and c determine the shape and position of the parabola represented by the quadratic equation.