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 does it mean to factor a quadratic expression?

Back

Factoring a quadratic expression means rewriting it as a product of two binomials, such as (px + q)(rx + s), where the product equals the original expression.

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 - r1)(x - r2) = 0, then set each factor equal to zero and solve for x.

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 expression: x² - 5x + 6

Back

(x - 2)(x - 3)

Front

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

Back

Make it equal to 0 by subtracting 3 from both sides.

Front

Solve by factoring: n² - 2n = 0

Back

n = 2 and n = 0

Front

Solve by factoring: x² - 7x - 18 = 0

Back

x = 9 and x = -2

Front

What is the factored form of the quadratic expression 2x² + 7x + 6?

Back

(2x + 3)(x + 2) = 0