Question

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

A. f(x) = 8 - x⁵
B. f(x) = -3x⁵ + 5x - 2
C. f(x) = 2x⁵ + 2x + x³
D. f(x) = x³ - 8x²

Answer 1

Options B and D are the polynomial functions written in standard form, as their terms are in descending order of degree. Option A requires reordering, and option C needs the terms to be ordered correctly to be in standard form.

Step-by-step explanation:

To determine which polynomial functions are written in standard form, we need to ensure the terms are ordered from the highest degree to lowest degree. The standard form of a polynomial function follows the pattern of anxn + an-1xn-1 + ... + a2x2 + a1x + a0, where ai are constants and the exponents decrease in value from left to right.

• B. f(x) = -3x5 + 5x - 2 is written in standard form because the terms are in order from the highest exponent to the lowest.
• D. f(x) = x3 - 8x2 is also in standard form with the terms in descending order of degree.

Options A and C are not in standard form:

• A. f(x) = 8 - x5 needs the terms reordered to x5 + 8.
• C. f(x) = 2x5 + 2x + x3 needs to be reordered to 2x5 + x3 + 2x.