Factoring Quadratic Equations

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 expressing it as a product of two binomials, such that when multiplied, they yield the original quadratic 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

What is the factored form of the quadratic equation 10x² + 9x - 7?

Back

(5x + 7)(2x - 1)

Front

What is the factored form of the quadratic equation 8x² + 22x + 5?

Back

(4x + 1)(2x + 5)

Front

What is the factored form of the quadratic equation 2x² - 15x + 27?

Back

(2x - 9)(x - 3)

Front

What is the factored form of the quadratic equation 2x² + 13x + 15?

Back

(2x + 3)(x + 5)

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 find the roots of a quadratic equation using factoring?

Back

To find the roots, factor the quadratic equation into binomials, set each factor equal to zero, and solve for x.

Front

What is a binomial?

Back

A binomial is a polynomial with exactly two terms, such as (x + 3) or (2x - 5).