Question

Which one of the following polynomial is in standard form?

A) 5x⁷ - x¹ + 2x⁴ - x²

B) 9x⁸ - 4x² + 1 - x⁵

C) 7x³ + 9x² - x² + 1 - x⁹

D) x⁶ - x⁴ - x² + 1

Answer 1

The polynomial D) x⁶ - x⁴ - x² + 1 is the one in standard form because its terms are written in descending order of their exponents.

Step-by-step explanation:

The question pertains to identifying which polynomial is in standard form. A polynomial is in standard form when its terms are written in descending order of their exponents. Assessing the options provided:

• A) 5x⁷ - x¹ + 2x⁴ - x² is not in standard form because the terms are not in descending order.
• B) 9x⁸ - 4x² + 1 - x⁵ is not in standard form because the terms are not in descending order.
• C) 7x³ + 9x² - x² + 1 - x⁹ is not in standard form because the terms are not in descending order, and there's a term that should be combined (9x² - x²).
• D) x⁶ - x⁴ - x² + 1 is in standard form because the terms are written in descending order of their exponents.

Therefore, the polynomial in standard form is D) x⁶ - x⁴ - x² + 1.