Terms and coefficient of polynomial — lesson. Mathematics CBSE, Class 9.

PUMPA - SMART LEARNING

எங்கள் ஆசிரியர்களுடன் 1-ஆன்-1 ஆலோசனை நேரத்தைப் பெறுங்கள். டாப்பர் ஆவதற்கு நாங்கள் பயிற்சி அளிப்போம்

Book Free Demo

Consider a polynomial in one variable(

$x$ ).

$p(x) =$

$a_{n}x^{n}$

$+$

$a_{n-1}x^{n-1}$

$+...$

$a_{2}x^{2}$

$+$

$a_{1}x$

$+a_{0}$

The terms of the polynomial

$p (x)$ are

$a_{n} x^{n}$ ,

$a_{n - 1} x^{n - 1}$ , ...,

$a_{0}$ .

The coefficient of the polynomial

$p (x)$ is

$a_{n}$ ,

$a_{n - 1}$ , …,

$a_{2}$ ,

$a_{1}$ of the variable

$x^{n}$ ,

$x^{n - 1}$ , ...,

$x^{2}$ ,

$x$ respectively.

Example:

1. Consider the polynomial

$p (x) = a x^{2} - 8 x + 9$ .

The terms of the polynomial are

$a x^{2}$ ,

$- 8 x$ ,

$9$ .

The coefficient of

$x^{2}$ is

$a$ .

The coefficient of

$x$ is

$-8$ .

The coefficient of

$x^{0}$ constant is

$9$ .

2. Consider the polynomial

$p (x) = {9 x}^{3} - {3 x}^{2} + 8 x - 2$ .

The terms of the polynomial are

$9x^{3}$ ,

$-3x^{2}$ ,

$8x$ and

$2$ .

The coefficient of

$x^{3}$ is

$9$ .

The coefficient of

$x^{2}$ is

$-3$ .

The coefficient of

$x$ is

$8$ .

And

$-2$ is the coefficient of

$x^{0}$ .

Important!

Polynomial may have any finite number of terms.

$p(x) =$

$x^{199}$

$+$

${4 x}^{198}$

$+$

$...$

$+$

$2x$

$+$

$3$ .

A polynomial of one term is defined as a monomial.

$p (x) = 8 x$ .

The two terms are referred to as binomial.

$p (x) = {9 x}^{3} + 3$ .

And the three terms are referred to as trinomial.

$p (x) = {7 x}^{4} + {3 x}^{3} + 7$ .

Constant polynomial: The constant polynomial is the form

$p(x) = c$ , where

$c$ is the actual number. This means that it is constant for all possible values of

$x$ ,

$p(x) = c$ . Polynomials

$p(x) = -3$ ,

$q(y) = 18$ ,

$r(z) = \frac{2}{5}$ are the examples of constant polynomial.

Zero polynomial: The constant polynomial

$0$ is called the zero polynomial.

$p(x)=0$ is the zero polynomial.

Previous theory

Exit to the topic

Next theory

Send feedback

Did you find an error?

Send it to us!

3. Terms and coefficient of polynomial

Theory: