College

Choose the expression that represents a linear expression.

A. [tex]\(-17x^4 - 18x^3 + 19x^2 - 20x + 21\)[/tex]

B. [tex]\(18x^3 + 19x^2 - 20x + 21\)[/tex]

C. [tex]\(23x^2 + 24x - 25\)[/tex]

D. [tex]\(4x + 4\)[/tex]

Answer :

Sure! Let's break down the expressions to determine which one is a linear expression.

1. A linear expression is a polynomial where the highest power of the variable is 1. In simple terms, it looks like this: [tex]\( ax + b \)[/tex], where [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are constants.

Let's examine each expression:

1. Expression: [tex]\(-17x^4 - 18x^3 + 19x^2 - 20x + 21\)[/tex]
- The term with the highest power is [tex]\(x^4\)[/tex].
- Since the highest power is 4, this expression is not linear.

2. Expression: [tex]\(18x^3 + 19x^2 - 20x + 21\)[/tex]
- The term with the highest power is [tex]\(x^3\)[/tex].
- Since the highest power is 3, this expression is not linear.

3. Expression: [tex]\(23x^2 + 24x - 25\)[/tex]
- The term with the highest power is [tex]\(x^2\)[/tex].
- Since the highest power is 2, this expression is not linear.

4. Expression: [tex]\(4x + 4\)[/tex]
- The term with the highest power is [tex]\(x\)[/tex], which is [tex]\(x^1\)[/tex].
- Since the highest power is 1, this expression is linear.

So, the linear expression is [tex]\(4x + 4\)[/tex].

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