Sure, let's break down the polynomial [tex]\( x + 4 \)[/tex] step by step.
1. Identify the Type and Number of Terms:
The expression [tex]\( x + 4 \)[/tex] consists of two parts:
- [tex]\( x \)[/tex] (a term involving the variable [tex]\( x \)[/tex])
- [tex]\( 4 \)[/tex] (a constant term)
A polynomial is classified based on the highest degree of its terms.
- For [tex]\( x + 4 \)[/tex], the highest degree term is [tex]\( x \)[/tex] (with degree 1).
Therefore, this polynomial is a linear polynomial because the highest power of the variable [tex]\( x \)[/tex] is 1.
There are 2 terms in this polynomial: [tex]\( x \)[/tex] and [tex]\( 4 \)[/tex].
2. Constant Term:
The constant term is the term that does not contain any variables. In this polynomial, it is [tex]\( 4 \)[/tex].
3. Leading Term:
The leading term is the term with the highest degree in the polynomial. Here, the highest degree term is [tex]\( x \)[/tex], which is the leading term.
4. Leading Coefficient:
The coefficient of the leading term (the numerical factor in front of the variable [tex]\( x \)[/tex]) is called the leading coefficient. In the term [tex]\( x \)[/tex], the implicit coefficient is [tex]\( 1 \)[/tex].
Putting it all together:
- The expression represents a linear polynomial with 2 terms.
- The constant term is 4.
- The leading term is [tex]\( x \)[/tex].
- The leading coefficient is 1.
So, the completed answer is:
The expression represents a linear polynomial with 2 terms. The constant term is 4, the leading term is [tex]\( x \)[/tex], and the leading coefficient is 1.
