The degree of the polynomial $p(x)=7x^{4}-3x^{3}+5x^{2}+x-9$ will be :

Question

Accepted Answer

The correct option is 2:

To determine the degree of a polynomial, we need to identify the term with the highest exponent of the variable.

Let's look at the given polynomial:
$p(x)=7x^{4}-3x^{3}+5x^{2}+x-9$

Break down the polynomial into its individual terms and their corresponding exponents:1.  First term: $7x^{4}$ has an exponent of $4$.
2.  Second term: $-3x^{3}$ has an exponent of $3$.
3.  Third term: $5x^{2}$ has an exponent of $2$.
4.  Fourth term: $x$ can be written as $x^{1}$, so it has an exponent of $1$.
5.  Fifth term: $-9$ is a constant term, which can be written as $-9x^{0}$, so it has an exponent of $0$.Now, compare all the exponents we found: $4, 3, 2, 1, 0$.
The highest exponent among these is $4$.
Therefore, the degree of the polynomial $p(x)=7x^{4}-3x^{3}+5x^{2}+x-9$ is $4$.

The incorrect option is 1:
This option suggests the degree is 1. This would be the case if the highest power of $x$ was $x^1$, which is not true for the given polynomial.

The incorrect option is 3:
This option suggests the degree is 0. This would be the case if the polynomial was a non-zero constant (e.g., $p(x) = -9$), which is not the given polynomial.

The incorrect option is 4:
This option is incorrect because there is a definite degree for the given polynomial, which is 4.