To solve the given questions, we need to carefully analyze the algebraic expression [tex]\(3x^2 - 4x^3 + 5x - 7\)[/tex].
### 1.1.1 Determining the Number of Terms in the Expression
An algebraic term in the expression is a part of the expression that is separated by plus (+) or minus (−) signs. Let's break down the given expression into its constituent terms:
1. [tex]\(3x^2\)[/tex]
2. [tex]\(-4x^3\)[/tex]
3. [tex]\(5x\)[/tex]
4. [tex]\(-7\)[/tex]
Each of these represents a distinct term in the expression. Hence, by counting these distinct parts, we find that there are 4 terms in the expression.
### 1.1.2 Identifying the Constant Term in the Expression
The constant term in an algebraic expression is the term that does not contain any variables (i.e., it does not have [tex]\(x\)[/tex] or any other variable associated with it). In the expression [tex]\(3x^2 - 4x^3 + 5x - 7\)[/tex], the term [tex]\(-7\)[/tex] does not involve the variable [tex]\(x\)[/tex]. Therefore, [tex]\(-7\)[/tex] is identified as the constant term.
Thus, the answers to the questions are:
- 1.1.1 There are 4 terms in the expression.
- 1.1.2 The constant term in the expression is [tex]\(-7\)[/tex].
