Table of Contents

## Why do we need to factor the polynomial?

Factoring is an important process that helps us understand more about our equations. Through factoring, we rewrite our polynomials in a simpler form, and when we apply the principles of factoring to equations, we yield a lot of useful information.

**What is the purpose of factoring numbers?**

Factoring is a common mathematical process used to break down the factors, or numbers, that multiply together to form another number.

**Why is factoring important in real life?**

Factoring is a useful skill in real life. Common applications include: dividing something into equal pieces, exchanging money, comparing prices, understanding time and making calculations during travel.

### How does factoring polynomials apply to real life?

It is used in bond trading and mortgage calculations. The polynomial is of high order, for example, with an interest term with exponent 360 for a 30-year mortgage. This is not a formula that can be factored. Instead, if the interest needs to be calculated, it is solved for by computer or calculator.

**What is a polynomial factor?**

A factor of polynomial P(x) is any polynomial which divides evenly into P(x). For example, x + 2 is a factor of the polynomial x2 – 4. The factorization of a polynomial is its representation as a product its factors.

**Why is factoring polynomial important in graphing polynomial functions?**

Because a polynomial function written in factored form will have an x-intercept where each factor is equal to zero, we can form a function that will pass through a set of x-intercepts by introducing a corresponding set of factors.

## What are the objectives of factoring?

Objectives of Factoring The important objectives are as follows: To relieve from the trouble of collecting receivables so as to concentrate on sales and other major areas of business. To minimize the risk of bad debts arising on account of non-realisation of credit sales. To adopt better credit control policy.

**What is polynomial division used for in real life?**

We can use the division of polynomials to find the length, and our knowledge that area is equal to the length multiplied by the width. Since we’re finding the length, we take the expression for area and divide it by the expression for the width.

**How does factoring polynomials help us solve polynomial equations?**

Factoring and the zero-product property allow us to solve equations. To solve a polynomial equation, first write it in standard form. Once it is equal to zero, factor it and then set each variable factor equal to zero. The solutions to the resulting equations are the solutions to the original.

### What is the most significant part of the factoring polynomials?

No matter how many terms a polynomial has, it is always important to check for a greatest common factor (GCF) first. If there is a GCF, it will make factoring the polynomial much easier because the number of factors of each term will be lower (because you will have factored one or more of them out!).

**What is the easiest way to factor polynomials?**

When a polynomial has four or more terms, the easiest way to factor it is to use grouping. In this method, you look at only two terms at a time to see if any techniques become apparent. For example, you may see a Greatest Common Factor (GCF) in two terms, or you may recognize a trinomial as a perfect square.

**What is the first step in factoring any polynomial?**

The first step when factoring any polynomial is to factor out the GCF. The GCF is the greatest common factor for all the terms of the polynomial. By factoring out the GCF first, the coefficients and constant term of the polynomial will be reduced.

## How do you calculate the factors of polynomials?

To factor a polynomial completely is to find the factors of least degree that, when multiplied together, make the original polynomial. Stated mathematically, to factor a polynomial P(x), is to find two or more polynomials, say Q(x) and R(x), of lesser degree such that P(x) = Q(x) · R(x).

**What is the purpose of factoring a polynomial?**

Factoring polynomials involves breaking up a polynomial into simpler terms (the factors) such that when the terms are multiplied together they equal the original polynomial. Factoring helps solve complex equations so they are easier to work with.