# Polynomial Formula

A polynomial formula is a formula that expresses the polynomial expression. The polynomial an expression that has two or more than two terms(algebraic terms) is known as a polynomial expression. A repetitive summation or subtraction of binomials or monomials forms a polynomial expression. A polynomial can have both like as well as unlike terms in it. Like terms in polynomials are the terms which have the same variable and same power and the terms that have different variables and different powers are known as, unlike terms. Let us see the polynomial formula in the following section along with the solved examples.

## What is Polynomial Formula?

The polynomial formula has variables with different power and the highest power of the variable on solving is known as the degree of the polynomial. The polynomial formula is also known as the standard form of the polynomial where the arrangement of the variables is according to the decreasing power of the variable in the formula.

### Polynomial Formula

Polynomial Formula is given by:

\(\left(a x^{n}+b x^{\{n-1\}}+c x^{\{n-3\}}+\ldots \ldots+r x+s\right)\)

Where

- a, b, c, ..., s are coefficients
- x is the variable
- n is the degree of the polynomial

Some basic formulas associated with the polynomial expression given above are,

1.F(x) = a_{n}(x^{n})

where

- a is the coefficient
- x is the variable
- n is the exponent

2. F(x) = a_{n}x^{n} + a_{n-1}x^{n-1} + a_{n-2}x^{n-2} + …….. + a_{1}x +a_{0 }= 0

3. F(x)=a_{n}x^{n}+..+rx+s

- n is a natural number

a_{n}−b_{n}=(a−b)(a_{n}−1+a_{n}−2b+…)

- n is even number

a_{n}+b_{n}=(a+b)(a_{n}−1−a_{n}−2b+…)

- n is odd number
- a
_{n}+b_{n}=(a+b)(a_{n}−1−an−2b+…)

### Applications of Polynomial Formula

It has applications in engineering, computer, management, business, and even in farming. Variables and constants are used to create expressions defining quantities that are known and unknown.

The polynomial equations are formed with variables, exponents, and coefficients. Polynomials can be solved by factoring them into either in terms of the degree or variables present in the given equation.

Let's take a quick look at a couple of examples to understand the polynomial formula better.

## Examples Using Polynomial Formula

**Example 1:** Find the factors of the given polynomial formula (x^{2}+12x+36).

**Solution:**

To find:

factors of the polynomial

(x^{2}+12x+36)

(x^{2}+2(6)x+6^{2})

(x+6)^{2}

**Answer: Factors of the polynomial (x ^{2}+12x+36) are (x+6) and (x+6).**

**Example 2:** Find the factors of the given polynomial formula (x^{2}+3x-28).

**Solution:**

To find:

factors of the polynomial

(x^{2}+3x-28)

(x^{2}+7x-4x-28)

(x(x+7)-4(x+7)

(x-4)(x+7)

**Answer: Factors of the polynomial (x ^{2}+11x+28) are (x-4) and (x+7)**

**Example 3: **Calculate the factors of the polynomial x^{2} – 6x + 9?

**Solution:**

x^{2} – 6x + 9

= x^{2} – 2(3x) + 3^{2}

= x^{2} – 2(3)(x) + 3^{2}

= (x – 3)^{2}

**Answer: Factors of the polynomial x ^{2} – 6x + 9 are (x – 3) and (x – 3).**

## FAQs on Polynomial Formula

### What Is the Polynomial Formula in Algebra?

Polynomial Formula is given as, \(\left(a x^{n}+b x^{\{n-1\}}+c x^{\{n-3\}}+\ldots \ldots+s x+1\right)\)

### What Is the Polynomial Formula For Quadratic Polynomial?

A quadratic polynomial is in the form of ax^{2} + bx + c where a, b and c are real numbers and are numeric coefficients, variable x is unknown for which we find the solution.

### What Is the General Polynomial Formula?

The general form of the polynomial formula is a\(_n\)x^{n }where a is the coefficient, x is the variable, n is the exponent. On the other hand, the polynomial formula in the expanded form is, \(\left(a x^{n}+b x^{\{n-1\}}+c x^{\{n-3\}}+\ldots \ldots+s x+1\right)\)

### What Is n In the Polynomial Formula?

In the polynomial formula, n refers to the degree of the polynomial. The term with the highest power of x represents the degree of the polynomial which can be represented as Deg(p(x)).