Question

Define polynomial with some examples.

Answer 1

Polynomial

An algebraic expression is of the form of a0+a1x+a2x2+.........+anx^n,where n is positive integer and the coefficients a0,a1,A2,.......an are constants with an is not equal to 0 is called a polynomial of degree.

A polynomial in X is denoted by p(x),q(x),g(x) etc.

Examples:

p(X)=x^2-3x+2 is a polynomial in X.

Similarly,the polynomial in two variables X and y are generally denoted by p(x,y) and polynomial in three variables is denoted by p(x,y,z).

Hope it helps

Good luck on your assignment...

Answer 2

A Polynomial can be expressed in terms that only have positive integer exponents and the operations of addition, subtraction, and multiplication. In other words, it must be possible to write the expression without division.

Explanation:

EXAMPLES :

• x2 + 2x +5 Since all of the variables have integer exponents that are positive this is a polynomial.

• 5x +1 Since all of the variables have integer exponents that are positive this is a polynomial.

• (x7 + 2x4 - 5) * 3x Since all of the variables have integer exponents that are positive this is a polynomial.

• 5x-2 +1 Not a polynomial because a term has a negative exponent

• 3x½ +2 Not a polynomial because a term has a fraction exponent

• (5x +1) ÷ (3x) Not a polynomial because of the division

• (6x2 +3x) ÷ (3x) Is actually a polynomial because it's possible to simplify this to 3x + 1 --which of course satisfies the requirements of a polynomial. (Remember the definition states that the expression 'can' be expressed using addition,subtraction, multiplication. So, if it's possible to simplify an expression into a form that uses only those operations and whose exponents are all positive integers...then you do indeed have a polynomial equation)

[Polynomial Equation- is simply a polynomial that has been set equal to]