Polynomials are algebraic expressions that include real numbers and variables. Division and square roots cannot be involved in the variables. The variables can only include addition, subtraction and multiplication.

Let x be a variable, n be a positive integer and a_{0}, a_{1},a_{2}... ,a_{n} be constants. Then,
f(x) = a_{n}x ^{n} + a_{n-1}x^{n-1}+ ... + a_{1}x + a_{0} is called a Poly-nomial in variable x.

Here, a_{n}x ^{n}, a_{n-1}x^{n-1}, ... , a_{1}x, a_{0} are known as terms and a_{n}, a_{n-1}, ..., a_{1},a_{0} are coefficients.

Examples

1) p(x) = 3x -2 -----> polynomial in variable x.

2) q(y) = 3y^{2} - 2y + 4 ------> is a poly-nomial in y.

3) f(u)= 1/2 u^{3} - 3u^{2} + 2u - 4 ----> is a poly-nomial in variable u.

Not a Poly-nomial : If the exponent of any term is less than 1 or negative.

Examples :

1) 2x^{2} - 3√x + 5

Solution :
It is not a poly-nomial because the exponent of one term is 1/2 which is less than 1.

2) 1/(x^{2} - 2x + 5)

Solution :
It is not a poly-nomial because the exponent is negative.

3) 2x^{3} - 3/x + 4

Solution :
As the exponent of 2nd term is -1 so it is not a poly-nomial.
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Practice

Q.1 Write any poly-nomial in x with degree 3.
Q.2 P(x) = x^{3} + 2^{3} - 4x + 8. Write the coefficient of x^{2}.
Q.3 In P(x) = 5x^{2} + x^{5} - 2x + 4 write the degree of poly-nomial.
Q.4 In P(x) = 1/2 x^{3} - 7x^{2} + 8x, state the number of terms and write each terms.
Polynomials