Question

Which polynomial functions are written in standard form? Select all that apply.

1) f(x) = 8 – x⁵
2) f(x) = –3x⁵ + 5x – 2
3) f(x) = 2x⁵ + 2x³
4) f(x) = x³ – 8x²

Answer 1

Polynomial functions 2), 3), and 4) are written in standard form with their terms ordered in descending powers of x.

Step-by-step explanation:

To determine which polynomial functions are written in standard form, we need to understand that a polynomial is in standard form when its terms are arranged in descending order of their power (exponent). The coefficients can be any real numbers, but the powers of x must decrease as we move from left to right across the term.

1. f(x) = 8 − x⁵ is not in standard form because the terms are in ascending order of their exponents.
2. f(x) = −3x⁵ + 5x − 2 is in standard form because the terms are in descending order of their exponents.
3. f(x) = 2x⁵ + 2x³ is in standard form though it's missing some lower degree terms, the existing terms are in the correct order.
4. f(x) = x³ − 8x² is also in standard form for the same reason as 3).

Therefore, the polynomial functions in standard form are 2), 3), and 4).