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Answer :
To determine which expression represents a linear expression, we need to understand what a linear expression is. A linear expression is a polynomial of degree 1. This means that the highest power of the variable [tex]\( x \)[/tex] is 1.
Let's analyze each option:
a) [tex]\(-17x^4 - 18x^3 + 19x^2 - 20x + 21\)[/tex]
- The highest power of [tex]\( x \)[/tex] here is 4, which is not 1. Therefore, this is not a linear expression.
b) [tex]\(18x^3 + 19x^2 - 20x + 21\)[/tex]
- The highest power of [tex]\( x \)[/tex] is 3, which is not 1. Hence, this is not a linear expression.
c) [tex]\(23x^2 + 24x - 25\)[/tex]
- The highest power of [tex]\( x \)[/tex] is 2, which is not 1. So, this is not a linear expression.
d) [tex]\(4x + 4\)[/tex]
- The highest power of [tex]\( x \)[/tex] is 1. Therefore, this is a linear expression.
Thus, the expression that represents a linear expression is option d: [tex]\(4x + 4\)[/tex].
Let's analyze each option:
a) [tex]\(-17x^4 - 18x^3 + 19x^2 - 20x + 21\)[/tex]
- The highest power of [tex]\( x \)[/tex] here is 4, which is not 1. Therefore, this is not a linear expression.
b) [tex]\(18x^3 + 19x^2 - 20x + 21\)[/tex]
- The highest power of [tex]\( x \)[/tex] is 3, which is not 1. Hence, this is not a linear expression.
c) [tex]\(23x^2 + 24x - 25\)[/tex]
- The highest power of [tex]\( x \)[/tex] is 2, which is not 1. So, this is not a linear expression.
d) [tex]\(4x + 4\)[/tex]
- The highest power of [tex]\( x \)[/tex] is 1. Therefore, this is a linear expression.
Thus, the expression that represents a linear expression is option d: [tex]\(4x + 4\)[/tex].
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