To determine which expression represents a linear expression, we need to understand the definition of a linear expression:
A linear expression is an algebraic expression in which the highest power of the variable [tex]\( x \)[/tex] is 1. In other words, a linear expression has the form:
[tex]\[ ax + b \][/tex]
where [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are constants.
Given the four expressions, let's analyze each to see which one is linear:
1. [tex]\(-17x^4 - 18x^3 + 19x^2 - 20x + 21\)[/tex]
- The highest power of [tex]\( x \)[/tex] in this expression is 4 (the term [tex]\(-17x^4\)[/tex]). Therefore, this is not a linear expression.
2. [tex]\(18x^3 + 19x^2 - 20x + 21\)[/tex]
- The highest power of [tex]\( x \)[/tex] in this expression is 3 (the term [tex]\(18x^3\)[/tex]). Therefore, this is not a linear expression.
3. [tex]\(23x^2 + 24x - 25\)[/tex]
- The highest power of [tex]\( x \)[/tex] in this expression is 2 (the term [tex]\(23x^2\)[/tex]). Therefore, this is not a linear expression.
4. [tex]\(4x + 4\)[/tex]
- The highest power of [tex]\( x \)[/tex] in this expression is 1 (the term [tex]\(4x\)[/tex]). Therefore, this is a linear expression.
Thus, the expression that represents a linear expression is:
[tex]\[ 4x + 4 \][/tex]
The answer is:
[tex]\[ 4x + 4 \][/tex]
