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Polynomial

An expression of the form a0xn + a1xn1 + a2xn2 + a3xn3 + ..... + an where a0, a1, a2, a3, ....., an are given numbers (real or complex), n is a non-negative integer and x is a variable is called a polynomial in x.

a0, a1, a2, a3, etc., are called the coefficients of xn, xn1, xn2, xn3, etc., respectively.

a0xn, a1xn1, a2xn2, a3xn3, ....., an are called the terms of the polynomial.

an is called the constant term. Clearly, it is also the coefficient of x0.

If a0 ≠ 0, the polynomial is said to be of degree n and the term a0xn is called the leading term.

The general form of a polynomial of degree 1 is a0x + a1where a0 ≠ 0.

The general form of a polynomial of degree 2 is a0x2 + a1x + a2 where a0 ≠ 0.

A non-zero constant a0 itself is said to be a polynomial of degree 0 while a polynomial all of whose coefficients are zero is said to be a zero polynomial and is denoted by 0 and no degree is assigned to it.

Since a polynomial is an expression containing the variable x, it is denoted by f(x), p(x) or g(x) etc.

The value of a polynomial f(x) for x = a where a is real number or a complex number is denoted by f(a).

In particular, if the coefficients a0, a1, a2, a3, .... of a polynomial f(x) be all real numbers, the polynomial f(x) is said to be a real polynomial.


Examples of polynomial:

(i) 7x2 + 5x - 3 is a polynomial in x of degree 2 or a quadratic polynomial in x.

(ii) 4x3 + 9x2 - 4x + 2 is a polynomial in x of degree 3 or a cubic polynomial in x.

(iii) 5 - 2x53 + 9x2 is an expression but not a polynomial, since it contains a term containing x53 , where 53 is not a non-negative integer. 

● Factorization









10th Grade Math

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