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## Definition Of Polynomial

A polynomial is a monomial or a sum or difference of two or more monomials.

### More About Polynomial

Polynomial function: A polynomial function is a function whose terms each contain a constant multiplied by a power of a variable.
P(x) = a0xn + a1xn-1 + .................+ an-2x2 + an-1x + an is a polynomial function
where a0, a1, a2,..., an are all real numbers and n is a non-negative integer.
Polynomial in one variable: a0xn + a1xn-1 + .................+ an-2x2 + an-1x + an is a polynomial in one variable.

### Example of Polynomial

• The following are few examples of polynomials.
2x - 7, 5x2 + 2x - 8, - 7y2 + 4y - 13, 4x2 + 16xy + 16y2

### Solved Example on Polynomial

#### Ques: Simplify the polynomial expression: (10x3 + 12x + 15) - (3x3 + 6x + 10)

##### Choices:

A. 7x3 + 18x + 25
B. 7x3 + 6x + 5
C. 7x6 + 18x2 + 25
D. 7x6 + 6x2 + 5
Correct Answer: B

### Solution:

Step 1: The given polynomial expression (10x3 + 12x + 15) - (3x3 + 6x + 10) can be simplified as 7x3 + 6x + 5. [Combine like terms.]