Question

Identify the terms, their coefficients for each of the following expressions: $1+x+x^2$

Answer 1

Step 1: Determine the terms in the expression

1. An algebraic expression is made up of variables, constants, and arithmetic operations on these entities.
2. A term can be a number, a variable, or a product or quotient of numbers and variables, but not addition and subtraction of these.
3. Terms are separated by addition or subtraction.

Given expression is $1+x+x^2$.

The terms in the expression are: $1$, $x$ and $x^2$.

Step 2: Determine the coefficients of the terms

A coefficient is the numerical factor of the term.

The numerical coefficients of the terms are:

$$\begin{gathered} 1\to 1 \\ x\to 1 \\ {x}^2\to 1 \end{gathered}$$

Therefore, the terms of the expression are $1$, $x$ and $x^2$ and their coefficients are $1$, $1$ and $1$ respectively.

Note:

When the coefficient is $1$, it is omitted in writing (if variables are present).