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Answer :
To identify a linear expression from the given options, we need to look for an expression that has the highest power of [tex]\(x\)[/tex] as 1. A linear expression typically follows the form [tex]\(mx + c\)[/tex], where [tex]\(m\)[/tex] and [tex]\(c\)[/tex] are constants.
Let's evaluate each expression:
1. Expression 1: [tex]\(-17x^4 - 18x^3 + 19x^2 - 20x + 21\)[/tex]
- Highest power of [tex]\(x\)[/tex]: 4
- Conclusion: Not linear, as it contains terms with powers greater than 1.
2. Expression 2: [tex]\(18x^3 + 19x^2 - 20x + 21\)[/tex]
- Highest power of [tex]\(x\)[/tex]: 3
- Conclusion: Not linear, as it contains terms with powers greater than 1.
3. Expression 3: [tex]\(23x^2 + 24x - 25\)[/tex]
- Highest power of [tex]\(x\)[/tex]: 2
- Conclusion: Not linear, as it contains terms with powers greater than 1.
4. Expression 4: [tex]\(4x + 4\)[/tex]
- Highest power of [tex]\(x\)[/tex]: 1
- Conclusion: Linear, since it is in the form [tex]\(mx + c\)[/tex].
Therefore, the expression that represents a linear expression is:
Expression 4: [tex]\(4x + 4\)[/tex]
This is a linear expression because its highest power of [tex]\(x\)[/tex] is 1.
Let's evaluate each expression:
1. Expression 1: [tex]\(-17x^4 - 18x^3 + 19x^2 - 20x + 21\)[/tex]
- Highest power of [tex]\(x\)[/tex]: 4
- Conclusion: Not linear, as it contains terms with powers greater than 1.
2. Expression 2: [tex]\(18x^3 + 19x^2 - 20x + 21\)[/tex]
- Highest power of [tex]\(x\)[/tex]: 3
- Conclusion: Not linear, as it contains terms with powers greater than 1.
3. Expression 3: [tex]\(23x^2 + 24x - 25\)[/tex]
- Highest power of [tex]\(x\)[/tex]: 2
- Conclusion: Not linear, as it contains terms with powers greater than 1.
4. Expression 4: [tex]\(4x + 4\)[/tex]
- Highest power of [tex]\(x\)[/tex]: 1
- Conclusion: Linear, since it is in the form [tex]\(mx + c\)[/tex].
Therefore, the expression that represents a linear expression is:
Expression 4: [tex]\(4x + 4\)[/tex]
This is a linear expression because its highest power of [tex]\(x\)[/tex] is 1.
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