Polynomial

Q1

What is a Polynomial?

A polynomial is an expression that consists of variables (or indeterminate), terms, exponents and constants. For example, 3x² -2x-10 is a polynomial.

Q2

What are terms, degrees and exponents in a polynomial?

If 2x² – 3x +19 is a polynomial, then;
Terms: 2x²,-3x & 19
Degree: 2 (the highest exponent of variable x)
Exponents: Power raised to variable x, i.e. 2 and 1.

Q3

What is the standard form of the polynomial?

A standard polynomial is the one where the highest degree is the first term, and subsequently, the other terms come. For example, x³ – 3x² + x -12 is a standard polynomial. So the highest degree here is 3, then comes 2 and then 1.

Q4

What is the degree of zero and constant polynomial?

The degree of zero polynomial is not defined while the degree of a constant polynomial is 1.

Q5

Is 8 a polynomial?

8 can be written as 8x⁰ or 0x²+0x+8, which represents the polynomial expression. Therefore, we can consider 8 as a polynomial.

Q6

How to add and subtract polynomials?

To add polynomials, always add the like terms, i.e. the terms having the same variable and power. The addition of polynomials always results in a polynomial of the same degree.
For example if we add x²+3x and 2x² + 2x + 9, then we get:
x²+3x+2x²+2x+9 = 3x²+5x+9. Subtracting polynomials is similar to addition, the only difference being the type of operation. So, subtract the like terms to obtain the solution. It should be noted that subtraction of polynomials also results in a polynomial of the same degree.
So,
x²+3x-(2x²+2x+9) = x²+3x-2x²-2x-9 = -x²+x-9