Question

Lin divides the polynomial 2 - 4r + 1 by 4 and obtains the result 0.522 - x + 0.25. Complete the explanation to determine whether 0.5r - x + 0.25 is indeed a polynomial.

Select the appropriate options:

A) It is a polynomial because all of the exponents are ________.
B) An expression is still a polynomial when the coefficients are ________.

Answer 1

A) It is a polynomial because all of the exponents are 1 or 0. B) An expression is still a polynomial when the coefficients are any real numbers.

Step-by-step explanation:

A polynomial is an expression consisting of variables, coefficients, and exponents, where the exponents are non-negative integers. In this case, the expression 0.5r - x + 0.25 is a polynomial because all of the exponents are 1 or 0, which are non-negative integers.

An expression is still a polynomial when the coefficients are any real numbers, including decimals and fractions. So, 0.5r - x + 0.25 is still a polynomial since the coefficients 0.5 and 0.25 are real numbers.