Question

Select ALL examples of a polynomial that is in standard form.

a) x³ + x + 3
b) x² – x³ + b
c) x² + y² + x + y + 4
d) 4x - 26

Answer 1

Polynomials in standard form from the given options are a) x³ + x + 3 and d) 4x - 26, as they have their terms ordered from highest to lowest degree.

Step-by-step explanation:

The question requires us to identify polynomials in standard form. A polynomial is in standard form when its terms are ordered from highest degree to lowest degree. Let's analyze the given examples:

• a) x³ + x + 3: This polynomial is in standard form because the powers on x are in descending order.
• b) x² - x³ + b: This is not in standard form because the terms are not in descending power order. It should be written as -x³ + x² + b.
• c) x² + y² + x + y + 4: This polynomial is not a single-variable polynomial and its terms are also not ordered by degree, so it is not in standard form.
• d) 4x - 26: This is a polynomial in standard form. Although it is a first-degree polynomial, or linear equation, the term with x comes before the constant term as required.

Therefore, the polynomials in standard form among the given examples are option a and option d.