Question

Find the degree of $2 - {y^2} - {y^3} + 2{y^8}$
A. 2
B. -1
c. 3
D. 8

Answer 1

Hint: A polynomial in one variable may have different powers, like the one given in the problem. The degree of the polynomial is the highest power to which the variable is raised. So, we will note all powers of the variable in the polynomial and the highest one will be the degree of the polynomial.

Complete step by step solution:
In the problem a polynomial expression is given to us as $2 - {y^2} - {y^3} + 2{y^8}$
Let the polynomial be
$p(y) = 2 - {y^2} - {y^3} + 2{y^8}$
So the polynomial is made up of one variable ‘y’ with different powers.
Now, in the polynomial $p(y)$ the different powers to which the variable y is raised are- 2, 3 and 8 with the following terms in the polynomial:
2 in $ - {y^2}$
3 in $ - {y^3}$
8 in $ + 2{y^8}$
So, the highest power to which the variable ‘y’ is raised is 8.
That is, the degree of the polynomial $p(y)$ is 8.
Therefore, the degree of $2 - {y^2} - {y^3} + 2{y^8}$ is 8.

So, the correct answer is option D.


Note: A polynomial can never have negative or fractional power(s). An algebraic expression in which the variable(s) are raised to the fractional or negative power is not a polynomial.