Factoring Quadratic Polynomials

Front

What is a quadratic polynomial?

Back

A quadratic polynomial is a polynomial of degree 2, typically in the form ax² + bx + c, 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 standard form of a quadratic polynomial?

Back

The standard form of a quadratic polynomial is ax² + bx + c.

Front

What is the general method for factoring quadratic polynomials?

Back

The general method involves finding two numbers that multiply to ac (the product of a and c) and add to b.

Front

What is the significance of the coefficients in a quadratic polynomial?

Back

The coefficients a, b, and c determine the shape and position of the parabola represented by the quadratic polynomial.

Front

What is the GCF (Greatest Common Factor) and how is it used in factoring?

Back

The GCF is the largest factor that divides all terms in a polynomial. It is used to simplify the polynomial before further factoring.

Front

How do you factor a quadratic polynomial when a = 1?

Back

When a = 1, you look for two numbers that add to b and multiply to c.

Front

What is the difference between factoring completely and partially?

Back

Factoring completely means breaking down a polynomial into its simplest factors, while partial factoring may leave some factors intact.

Front

What is a perfect square trinomial?

Back

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

Front

What is the role of the discriminant in factoring quadratics?

Back

The discriminant (b² - 4ac) determines the nature of the roots of the quadratic equation and can indicate whether it can be factored over the reals.