Classify the expression: [tex]$5 x+2$[/tex].
A. Linear expression
B. Quadratic expression
C. Cubic expression
D. Quartic expression
Answer (2)
L in e a re x p ress i o n
Explanation
Understanding the Problem We are asked to classify the expression 5 x + 2 . This involves identifying the type of polynomial expression based on its degree.
Determining the Degree The given expression is 5 x + 2 . The degree of a polynomial is the highest power of the variable in the expression. In this case, the variable is x , and its highest power is 1 (since x is the same as x 1 ).
Classifying the Expression Since the degree of the expression 5 x + 2 is 1, it is a linear expression. A linear expression has the general form a x + b , where a and b are constants.
Final Answer Therefore, the expression 5 x + 2 is a linear expression.
Examples
Linear expressions are used in many real-life situations. For example, the cost of a taxi ride can be modeled as a linear expression, where the cost is a fixed amount plus a variable amount depending on the distance traveled. If the fixed cost is $2 and the variable cost is 0.50 p er mi l e , t h e n t h e t o t a l cos t f or x$ miles is given by the linear expression 2 + 0.50 x .
The expression 5 x + 2 is classified as a linear expression because its degree is 1. Linear expressions are typically in the form a x + b . Therefore, the answer is A. Linear expression.
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