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 means rewriting it as a product of two binomials, such as (x + p)(x + q) = 0, where p and q are the roots of the equation.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0.

Front

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

Back

To find the roots, factor the quadratic into the form (x + p)(x + q) = 0, then set each factor equal to zero: x + p = 0 and x + q = 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.

Front

Factor the quadratic: x² + 10x + 16

Back

(x + 2)(x + 8)

Front

Solve by factoring: x² - 9x + 20 = 0

Back

x = 4 and x = 5

Front

Solve by factoring: x² - 6x = -8

Back

x = 2 and x = 4

Front

What is the first step in solving the equation x² + 6x - 13 = 3?

Back

Make it equal 0 by subtracting 3 on each side.

Front

What are the coefficients in the quadratic equation ax² + bx + c?

Back

The coefficients are a (the coefficient of x²), b (the coefficient of x), and c (the constant term).