Question

Write the degree of each of the following polynomials:
i.$5{x^3} + 4{x^2} + 7x$
ii.$4 - {y^2}$
iii.$5t - \sqrt 7 $
iv.$3$

Answer 1

Hint: Recall that the degree of the polynomial is the highest degree of the variable present in the given expression. Degree, here, refers to the power of the variable. For example, in a polynomial ${x^5} + {x^3} + 1$ , the degree will be $5$ because the highest power of $x$ in this expression is $5$. Try to solve the above questions applying this similar logic.

Complete step-by-step answer:
(i): $5{x^3} + 4{x^2} + 7x$
Here, $x$ is the variable. In the three terms of this expression, the power of $x$ is $3,2$ and $1$ respectively. The highest power is $3$ . Therefore the degree of the polynomial is $3$.
(ii): $4 - {y^2}$
The variable in this question is $y$ . The expression can also be written as $4{y^0} - {y^2}$ because any variable or number raised to the power $0$ is $1$ . Therefore, the power of $y$ in the individual terms is $0$ and $1$ respectively. Since the highest power is $1$ , the degree of this polynomial is $1$ .
(iii): $5t - \sqrt 7 $
The variable in this question is $t$ . Similar to the previous question, we can write it as $5{t^1} - \sqrt 7 {t^0}$. The power of $t$ in the individual terms is $1$ and $0$ respectively. So the degree of this polynomial is 1 since the highest power is $1$.
 (iv): $3$
This is a constant number. But this can be written as $3 \times 1$ . There is no variable in this expression but that also implies that if there had been a variable present, it’s power would have been $0$ because any variable to the power $0$ is $1$. Therefore, the degree of this polynomial is $0$.

Note: Whenever a polynomial expression is given and the variable is missing from any of the terms, assume that the variable has degree zero in that term. Basically, anything, number or variable, raised to the power $0$ is $1$. Apart from this, to arrive at the correct solution, just check the greatest power of the variable in the expression and will only be the degree of the polynomial.