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Answer :
To determine which expression represents a linear expression, we need to understand what makes an expression linear. A linear expression is a polynomial of degree 1, which means the highest power of the variable [tex]\( x \)[/tex] is 1.
Let's analyze each of the given expressions:
1. Expression: [tex]\(-17x^4 - 18x^3 + 19x^2 - 20x + 21\)[/tex]
- The highest power of [tex]\( x \)[/tex] is 4.
2. Expression: [tex]\(18x^3 + 19x^2 - 20x + 21\)[/tex]
- The highest power of [tex]\( x \)[/tex] is 3.
3. Expression: [tex]\(23x^2 + 24x - 25\)[/tex]
- The highest power of [tex]\( x \)[/tex] is 2.
4. Expression: [tex]\(4x + 4\)[/tex]
- The highest power of [tex]\( x \)[/tex] is 1.
From these evaluations:
- The first expression has a degree of 4 (not linear).
- The second expression has a degree of 3 (not linear).
- The third expression has a degree of 2 (not linear).
- The fourth expression has a degree of 1.
Therefore, the expression [tex]\(4x + 4\)[/tex] is a linear expression because it has the highest power of [tex]\( x \)[/tex] equal to 1.
Let's analyze each of the given expressions:
1. Expression: [tex]\(-17x^4 - 18x^3 + 19x^2 - 20x + 21\)[/tex]
- The highest power of [tex]\( x \)[/tex] is 4.
2. Expression: [tex]\(18x^3 + 19x^2 - 20x + 21\)[/tex]
- The highest power of [tex]\( x \)[/tex] is 3.
3. Expression: [tex]\(23x^2 + 24x - 25\)[/tex]
- The highest power of [tex]\( x \)[/tex] is 2.
4. Expression: [tex]\(4x + 4\)[/tex]
- The highest power of [tex]\( x \)[/tex] is 1.
From these evaluations:
- The first expression has a degree of 4 (not linear).
- The second expression has a degree of 3 (not linear).
- The third expression has a degree of 2 (not linear).
- The fourth expression has a degree of 1.
Therefore, the expression [tex]\(4x + 4\)[/tex] is a linear expression because it has the highest power of [tex]\( x \)[/tex] equal to 1.
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