Factoring Polynomials

Front

What is the process of factoring a polynomial?

Back

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

Front

What is the Greatest Common Factor (GCF) in factoring?

Back

The GCF is the largest factor that divides all terms in a polynomial, and it is often factored out first to simplify the expression.

Front

How do you factor a quadratic polynomial of the form ax^2 + bx + c?

Back

To factor a quadratic polynomial, find two numbers that multiply to ac (the product of a and c) and add to b. Use these numbers to split the middle term and factor by grouping.

Front

What is the difference between factoring completely and factoring partially?

Back

Factoring completely means breaking down a polynomial into its irreducible factors, while factoring partially may involve factoring out a GCF or a simple binomial but not fully simplifying the expression.

Front

What are the steps to factor the polynomial 2x^2 - 2x - 6?

Back

1. Factor out the GCF (2). 2. Factor the quadratic x^2 - x - 3 using the quadratic formula or by finding factors.

Front

What is a binomial?

Back

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

Front

What is a trinomial?

Back

A trinomial is a polynomial that consists of exactly three terms, such as (x^2 + 5x + 6).

Front

How do you factor the trinomial k^2 + 7k + 10?

Back

Look for two numbers that multiply to 10 and add to 7. The factors are (k + 2)(k + 5).

Front

What is the significance of the quadratic formula in factoring?

Back

The quadratic formula can be used to find the roots of a quadratic equation, which can help in factoring the polynomial.

Front

What does it mean to factor by grouping?

Back

Factoring by grouping involves rearranging and grouping terms in a polynomial to factor out common factors from each group.