Question

How do you identify the terms in the polynomial expression, $6{x^3} - 5x + 2$ and give the degree of each term?

Answer 1

Polynomials are sums of variables and exponents expressions. Each piece of the polynomial that is, each part that is being added or subtracted is called a "term".
For example, $a{x^2} + bx + c$ where $a{x^2}$, $bx$, $c$ are the terms of the polynomial each term is added.
Degree of the polynomial defined as the highest power of a variable in a polynomial.
In this question, there are three terms separated by the plus and minus.
The degree of the first term is the power of ${x^3}$.
The degree of the second term is the power $x$.
The degree of the constant is always $0$ .

Complete step-by-step answer:
Consider the polynomial expression is given as $6{x^3} - 5x + 2$.
The terms of polynomials are the parts of the equation that are generally separated by “+” or “-” signs.
The first term of the polynomial expression is $6{x^3}$.
The second term of the polynomial expression is $- 5x$.
The third term of the polynomial expression is $2$.
A polynomial’s degree is the highest or the greatest power of a variable in a polynomial equation.
The degree of each term is the power of the variable present in the term.
The degree of term $6{x^3}$ is$3$.
The degree of term $- 5x$ is $1$.
The degree of term $2$ that is $2{x^0}$ is $0$.

Final answer: The terms of the polynomial expression, $6{x^3} - 5x + 2$ are $6{x^3}$,$- 5x$,$2$and corresponding degree is $3$, $1$ and $0$ respectively.

Note:
The degree of the polynomial with one variable is the higher power of the polynomial expression. But, if a polynomial with multiple variables, the degree of the polynomial can be found by adding the powers of different variables in any terms present in the polynomial expression.
Ex: ${x^3}{y^4} + 2x{y^2} + {x^2}$
In ${x^3}{y^4}$, the first term degree is $3 + 4 = 7$ .
In $2x{y^2}$, the degree of the second term is $1 + 2 = 3$ .
In ${x^2}$ , the degree of the third term is $2$.
The degree of the polynomial is the highest power of the polynomial that is $7$ .