Solving Quadratics by factoring

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What does it mean to factor a polynomial?

Back

Factoring a polynomial means expressing it as a product of its factors, which are polynomials of lower degrees.

Front

What is the first step in solving a quadratic equation by factoring?

Back

The first step is to set the equation to zero and check if there is a greatest common factor (GCF) that can be factored out.

Front

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

Back

Set each factor equal to zero and solve for the variable.

Front

What is the relationship between the coefficients and the roots of a quadratic equation?

Back

For a quadratic equation ax² + bx + c = 0, the sum of the roots is -b/a and the product of the roots is c/a.

Front

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

Back

The discriminant (b² - 4ac) determines the nature of the roots: if it's positive, there are two distinct real roots; if zero, one real root; if negative, two complex roots.

Front

What are the steps to factor the quadratic x² + 2x - 24?

Back

1. Identify two numbers that multiply to -24 (the constant term) and add to 2 (the coefficient of x). 2. The numbers are 6 and -4. 3. Factor as (x + 6)(x - 4) = 0.

Front

How do you check if your factored form is correct?

Back

You can check by expanding the factors back to the original quadratic equation.

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a quadratic expression that can be factored into the square of a binomial, such as (a + b)² = a² + 2ab + b².

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.