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.

Tags

CCSS.HSF-IF.C.7A

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.

Tags

CCSS.HSA.APR.C.4

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.

Tags

CCSS.HSA-REI.B.4B