Select all of the following expressions that are polynomials.(2 points) Responses 12x3+2x2−5 1 half x cubed plus 2 x squared minus 5 3x12+10 3 x raised to the 1 half power plus 10 4x−2+9x+6 4 x to the negative 2 power plus 9 x plus 6 −4x+1

Answer 1

A polynomial is an expression that consists of variables raised to whole number (non-negative integer) powers and has coefficients that are real numbers. Let's analyze the given responses one by one:

1. 12x³ + 2x² - 5
   This is a polynomial because all the terms have non-negative integer powers (3 and 2).

2. 3x^(1/2) + 10
   This is not a polynomial because the term \(x^{1/2}\) has a fractional exponent.

3. 4x^(-2) + 9x + 6
   This is not a polynomial because the term \(4x^{-2}\) has a negative exponent.

4. −4x + 1
   This is a polynomial because it consists of terms with non-negative integer powers (1 and 0).

Based on this analysis, the polynomial expressions from the responses are:

• 12x³ + 2x² - 5
• −4x + 1