- Books Name
- CBSE Class 7 Mathematics Book

- Publication
- Param Publication

- Course
- CBSE Class 7

- Subject
- Mathmatics

**Polynomial**

A **polynomial **is an algebraic expression with one or more terms.

**For example :** 6x, x^{3} + 3x^{2} + 9x + 7, 3x^{2} – 4xy + 7y^{2} etc. are all polynomials.

**Degree of polynomial**

The degree of a polynomial of one variable is the highest power of the variable in the given polynomial. For example P(x) = 2x^{3} + 3x^{2} – 6x + 4. The highest power of x in all terms of polynomial is 3.

Hence, the degree of the polynomial is 3.

We can classify polynomial according to its degree.

** (i) Constant polynomial :** Polynomial having degree zero is known as **constant polynomial. **

**(ii) Linear polynomial : **Polynomial having degree one is known as linear polynomial.

For ex : 2x – 5, x + 3.

**(iii) Quadratic polynomial :** Polynomial having degree two is known as quadratic polynomial.

For ex : x^{2} + 1, 7x^{2}, x^{2 }+ 2x – 1.

**(iv) Cubic polynomial :** Polynomial having degree three is known as cubic polynomial.

For ex : 7x^{3} + 5x^{2} + 1, x^{3} – x + 1.

**(v) Biquadratic polynomial :** Polynomial having degree four is known as biquadratic polynomial.

For ex : x^{4} + 1, x^{4} + x^{2} + 1.

**Factors : **Each term in an algebraic expression is a product of one or more number(s) and/or literal number(s).

These number(s) and/or literal number(s) are known as the factors of that term.

(i) In the binomial 8ab + 3c, 8ab and 3c are two terms. In the term 8ab, 8, a and b are its factors. Clearly, number 8 is the numerical factor, and a and b are literal factors.

(ii) In the binomial expression – ab – 5, the term – ab has – 1 as the numerical factor while a and b are literal factors.

**Coefficient :** In a term of an algebraic expression any of the factors with the sign of the term is called the coefficient of the product of the factors.

Consider the term – 5ab in the binomial – 5ab + 7. The coefficient of a in the term – 5ab is – 5b, the coefficient of b is – 5a and the coefficient of ab is – 5.

- Books Name
- class 7 Mathematics Book

- Publication
- ReginaTagebücher

- Course
- CBSE Class 7

- Subject
- Mathmatics

**Types of algebraic expressions. Polynomials**

**Polynomial (poly - 'many', nomial - 'term').**

When an algebraic expression has one or many terms, then that expression is called a polynomial expression.

In some cases, polynomial multiplication can be performed easier when using the abridged multiplication formulas.

**You need to remember 3 formulas:**

**1) The square of the sum of two expressions:**

(a+b)^{2}=a^{2}+2ab+b^{2}

**2) The square of the difference of two expressions:**

(a−b)^{2}=a^{2}−2ab+b^{2}

**3) The difference of squares of two expressions:**

(a−b)(a+b)=a^{2}−b^{2}

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###### Medha Sharma

Course : CBSE Class 7

Start Date : 05.02.2023

End Date : 18.07.2023

Types of Batch : Classroom