1. Solve by Factoring or Extracting Roots

Front

What does it mean to solve an equation by factoring?

Back

Solving an equation by factoring involves rewriting the equation in a product form, allowing us to set each factor equal to zero to find the solutions.

Front

What is the Zero Product Property?

Back

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 (a)(b) = 0.

Front

Solve for x: (x - 3)(x + 6) = 0

Back

x = 3 or x = -6.

Front

What is the first step in factoring a quadratic equation?

Back

The first step is to look for a common factor (GCF) in all terms of the equation.

Front

Solve for x: 3x^2 + 18x + 15 = 0

Back

x = -5 or x = -1.

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax^2 + bx + c = 0.

Front

How do you find the roots of a quadratic equation?

Back

You can find the roots by factoring, using the quadratic formula, or completing the square.

Front

Solve for x: x^2 - 9 = 0

Back

x = 3 or x = -3.

Front

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

Back

The discriminant (b^2 - 4ac) determines the nature of the roots: if positive, there are two distinct real roots; if zero, one real root; if negative, no real roots.

Front

Solve for x: x^2 + 5x + 6 = 0

Back

x = -2 or x = -3.