Which of the following describes a polynomial that is not a polynomial function?
Practice Questions
Q1
Which of the following describes a polynomial that is not a polynomial function?
x^2 + 3x - 5
1/x + 2
3x^3 - 4x + 1
2x^4 + x^2
Questions & Step-by-Step Solutions
Which of the following describes a polynomial that is not a polynomial function?
Step 1: Understand what a polynomial is. A polynomial is an expression made up of variables raised to whole number powers and coefficients.
Step 2: Identify what a polynomial function is. A polynomial function is a polynomial that can be written in the form f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where n is a non-negative integer and a_n, a_(n-1), ..., a_0 are constants.
Step 3: Look at the expression given in the question: 1/x + 2.
Step 4: Rewrite 1/x as x^(-1). This shows that it has a negative exponent.
Step 5: Remember that polynomial functions cannot have negative exponents. They can only have whole number exponents.
Step 6: Conclude that since 1/x + 2 contains a term with a negative exponent (x^(-1)), it is not a polynomial function.
