Answer :
To determine which expression represents a linear expression, we need to look for the expression that has a maximum power of 1 for its variable, [tex]\( x \)[/tex]. A linear expression is typically of the form [tex]\( ax + b \)[/tex], where [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are constants, and the highest power of [tex]\( x \)[/tex] is 1.
Let's examine each of the given expressions:
1. [tex]\(-17x^4 - 18x^3 + 19x^2 - 20x + 21\)[/tex]
- This expression includes terms with [tex]\( x \)[/tex] raised to the powers of 4, 3, 2, and 1. The highest power is 4, which means it is not a linear expression.
2. [tex]\(18x^3 + 19x^2 - 20x + 21\)[/tex]
- This expression includes terms with [tex]\( x \)[/tex] raised to the powers of 3, 2, and 1. The highest power is 3, which means it is not a linear expression.
3. [tex]\(23x^2 + 24x - 25\)[/tex]
- This expression includes terms with [tex]\( x \)[/tex] raised to the powers of 2 and 1. The highest power is 2, which means it is not a linear expression.
4. [tex]\(4x + 4\)[/tex]
- This expression has [tex]\( x \)[/tex] raised to the power of 1. The highest power is 1, which means it is a linear expression.
After evaluating all the expressions, the one that represents a linear expression is [tex]\( 4x + 4 \)[/tex].
Let's examine each of the given expressions:
1. [tex]\(-17x^4 - 18x^3 + 19x^2 - 20x + 21\)[/tex]
- This expression includes terms with [tex]\( x \)[/tex] raised to the powers of 4, 3, 2, and 1. The highest power is 4, which means it is not a linear expression.
2. [tex]\(18x^3 + 19x^2 - 20x + 21\)[/tex]
- This expression includes terms with [tex]\( x \)[/tex] raised to the powers of 3, 2, and 1. The highest power is 3, which means it is not a linear expression.
3. [tex]\(23x^2 + 24x - 25\)[/tex]
- This expression includes terms with [tex]\( x \)[/tex] raised to the powers of 2 and 1. The highest power is 2, which means it is not a linear expression.
4. [tex]\(4x + 4\)[/tex]
- This expression has [tex]\( x \)[/tex] raised to the power of 1. The highest power is 1, which means it is a linear expression.
After evaluating all the expressions, the one that represents a linear expression is [tex]\( 4x + 4 \)[/tex].
