- Books Name
- CBSE Class 7 Mathematics Book
- Param Publication
- CBSE Class 7
A polynomial is an algebraic expression with one or more terms.
For example : 6x, x3 + 3x2 + 9x + 7, 3x2 – 4xy + 7y2 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) = 2x3 + 3x2 – 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 : x2 + 1, 7x2, x2 + 2x – 1.
(iv) Cubic polynomial : Polynomial having degree three is known as cubic polynomial.
For ex : 7x3 + 5x2 + 1, x3 – x + 1.
(v) Biquadratic polynomial : Polynomial having degree four is known as biquadratic polynomial.
For ex : x4 + 1, x4 + x2 + 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.