Answer :
To determine which expression represents a linear expression, let's first understand what a linear expression is.
A linear expression is an algebraic expression in which the highest power of the variable is 1. In other words, it is written in the form [tex]\( ax + b \)[/tex], where [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are constants, and [tex]\( x \)[/tex] is the variable.
Now, let's examine each option:
1. [tex]\(-17x^4 - 18x^3 + 19x^2 - 20x + 21\)[/tex]:
- This expression contains terms with powers as high as 4 ([tex]\(x^4\)[/tex]), making it a polynomial of degree 4.
2. [tex]\(18x^3 + 19x^2 - 20x + 21\)[/tex]:
- The highest power here is 3 ([tex]\(x^3\)[/tex]), so this is a polynomial of degree 3.
3. [tex]\(23x^2 + 24x - 25\)[/tex]:
- The highest power is 2 ([tex]\(x^2\)[/tex]), so this is a polynomial of degree 2.
4. [tex]\(4x + 4\)[/tex]:
- The highest power of [tex]\( x \)[/tex] in this expression is 1, making it a linear expression.
Among these options, the expression [tex]\( 4x + 4 \)[/tex] is the only one that has a variable raised to the first power, which satisfies the condition for a linear expression. Therefore, [tex]\( 4x + 4 \)[/tex] is the correct choice for a linear expression.
A linear expression is an algebraic expression in which the highest power of the variable is 1. In other words, it is written in the form [tex]\( ax + b \)[/tex], where [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are constants, and [tex]\( x \)[/tex] is the variable.
Now, let's examine each option:
1. [tex]\(-17x^4 - 18x^3 + 19x^2 - 20x + 21\)[/tex]:
- This expression contains terms with powers as high as 4 ([tex]\(x^4\)[/tex]), making it a polynomial of degree 4.
2. [tex]\(18x^3 + 19x^2 - 20x + 21\)[/tex]:
- The highest power here is 3 ([tex]\(x^3\)[/tex]), so this is a polynomial of degree 3.
3. [tex]\(23x^2 + 24x - 25\)[/tex]:
- The highest power is 2 ([tex]\(x^2\)[/tex]), so this is a polynomial of degree 2.
4. [tex]\(4x + 4\)[/tex]:
- The highest power of [tex]\( x \)[/tex] in this expression is 1, making it a linear expression.
Among these options, the expression [tex]\( 4x + 4 \)[/tex] is the only one that has a variable raised to the first power, which satisfies the condition for a linear expression. Therefore, [tex]\( 4x + 4 \)[/tex] is the correct choice for a linear expression.
