Table of Contents
Polynomial – Introduction, Rules, Types, and Formula
A polynomial is an expression made up of one or more terms, each of which is a product of a number (the coefficient) and one or more variables raised to a power (the exponents). The degree of a polynomial is the sum of the exponents of the variables. Polynomials can be added, subtracted, multiplied, and divided, just like ordinary numbers.
The following are some basic rules of polynomial operations:
• To add or subtract polynomials, add or subtract the coefficients of like terms and combine the variables according to their exponents.
• To multiply polynomials, multiply the coefficients of like terms and combine the variables according to their exponents.
• To divide polynomials, divide the coefficients of like terms and combine the variables according to their exponents.
The following are some examples of polynomial operations:
3×2 – 2x – 5
This polynomial is in standard form, with the coefficient of the x2 term first, the coefficient of the x term second, and the constant term last.
3×2 – 2x – 5
= (3×2 – 2x) + (-5)
= x2 – 2x – 8
2×2 + 3x – 5
= (2×2 + 3x) – 5
= 4×2
Table of Content
1.0 Introduction
1.1 Background
1.2 Objectives
1.3 Methodology
1.4 Limitations
2.0 Literature Review
3.0 Data Analysis
4.0 Findings
5.0 Conclusion
References
1.0 Introduction
The main objective of this research paper is to study the impact of foreign direct investment (FDI) on economic growth in Pakistan. The research will also investigate the factors that affect the level of FDI in Pakistan. In order to achieve the objectives of the study, the literature review section will first discuss the concept of FDI and its importance for the economy. The data analysis section will then present the findings of the study. Finally, the conclusion section will summarize the main findings of the research.
1.1 Background
Pakistan is one of the most populous countries in the world and has a large economy. However, the country has faced several challenges in recent years, including high levels of poverty, inequality, and unemployment. In addition, the country has been struggling with a high level of debt and a current account deficit.
One of the ways to address these challenges is to increase foreign investment in the country. Foreign direct investment (FDI) is a key component of economic development and can play a significant role in promoting economic growth. FDI is a type of foreign investment that involves the acquisition of a controlling interest in a
What is a Polynomial?
A polynomial is an expression consisting of one or more terms, each of which is a product of a constant and a variable raised to a positive integer power.
Rules for an Expression to be a Polynomial
An expression is a polynomial if it is in the form of axn+bxn-1+cxn-2+…+dx+e, where a, b, c, …, d, and e are real numbers and x is a real variable.
Terminologies in Polynomial Definition-
A polynomial is an expression consisting of variables and coefficients, that is, constants that are multiplied by the variables. The coefficients are the numbers that appear in front of the variables.
A degree of a polynomial is the largest degree of any one of the variables in the polynomial.
A leading coefficient of a polynomial is the coefficient of the variable with the highest degree.
A constant term of a polynomial is the term that has no variable.
A variable term of a polynomial is the term that has a variable.
Now you Might Think about what A Constant is?
A constant is an unchanging value or quantity.
Degree of a Polynomial
The degree of a polynomial is the highest power of the variable in the polynomial.
Types of Polynomial –
There are three types of polynomial: linear, quadratic, and cubic.
Linear polynomial: A linear polynomial is a polynomial in which the highest degree of the polynomial is one. In other words, a linear polynomial is a polynomial that consists of a single term.
Quadratic polynomial: A quadratic polynomial is a polynomial in which the highest degree of the polynomial is two. In other words, a quadratic polynomial is a polynomial that consists of two terms.
Cubic polynomial: A cubic polynomial is a polynomial in which the highest degree of the polynomial is three. In other words, a cubic polynomial is a polynomial that consists of three terms.
What is a Monomial?
A Monomial is an algebraic term consisting of a single numerical coefficient and a single variable, with no intervening operators.
What is a Binomial?
A binomial is a mathematical term for a two-part equation.
What is a Trinomial?
A Trinomial is a three-term algebraic expression.
Degree of a Polynomial-
A degree of a polynomial is the highest degree of any of the terms in the polynomial. The degree of a polynomial is also the value of the highest power in the polynomial.
What do you mean by the degree of a Zero Polynomial?
A zero polynomial is a polynomial that has a degree of zero. This means that the polynomial consists of a single term, and that term is zero.
What do you mean by Constant Polynomials?
Constant polynomials are polynomials in which all of the coefficients are constants.
Solving Polynomials-
A polynomial is an algebraic expression that can be written in the form:
ax^n + bx^n-1 + cx^n-2 + … + dx + e
Where a, b, c, d, and e are constants and x is the variable.
The degree of a polynomial is the largest exponent of x in the polynomial.
The roots of a polynomial are the values of x that make the polynomial equal to zero.
To solve a polynomial, you need to find all of its roots. There are several methods for doing this.
One method is to use the quadratic equation. This equation can be used to solve polynomials of degree two or less.
Another method is to use the synthetic division. This can be used to solve polynomials of degree three or less.
If the polynomial is of degree four or greater, then you can use the polynomial long division.
How to Solve Linear Polynomials?
Polynomials are equations that contain one or more variables and coefficients. Linear polynomials are polynomials in which the highest power of the variable is one. To solve a linear polynomial, you must first isolate the variable. This is done by removing the coefficients of the variable from both sides of the equation. Once the variable is isolated, you can solve the equation using basic algebraic methods.
How to Solve Linear Polynomials?
To solve a linear polynomial, you need to determine the roots of the equation. This can be done using a variety of methods, including graphing, factoring, and using the quadratic formula. Once the roots are determined, you can then solve for the equation’s coefficients.
Questions to be solved-
1. What is the value of the expression (x + y)2 – (x – y)2?
2. What is the value of the expression (x + y)2 + (x – y)2?
3. What is the value of the expression x2 + y2?
