Question

F(x) = 8x⁴ − πx² 14 determine whether f(x) is a polynomial or not. select the correct choice below and, if necessary, fill in the answer box to complete your choice.

Answer 1

The given function F(x) = 8x⁴ - πx² + 14 is a polynomial.

Step-by-step explanation:

A polynomial is an algebraic expression consisting of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents. The function F(x) = 8x⁴ - πx² + 14 fits this definition because it is a sum of terms where each term is a constant multiplied by a non-negative power of x.

Breaking down the function:

8x⁴ is a term with the variable x raised to the non-negative power of 4.

πx² is a term with the variable x raised to the non-negative power of 2.

14 is a constant term.

Since each term involves only multiplication by non-negative integer powers of x, and the operations are limited to addition and subtraction, the given function is indeed a polynomial.

In conclusion, F(x) = 8x⁴ - πx² + 14 satisfies the criteria of a polynomial, making the final answer affirmative.