Question

which polynomial is in standard form?
9+2x−8x⁴+16x⁵
12x⁵−6x²−9x+12
13x⁵+11x−6x²+5
7x⁷+14x⁹−17x+25

Explanation:

A polynomial in standard form is written with terms ordered from the highest degree of the variable to the lowest. We check each option:

1. $9+2x-8x^4+16x^5$: Ordered from lowest to highest degree, not standard.
2. $12x^5-6x^2-9x+12$: Ordered from highest degree ($x^5$) down to constant term, which follows standard form.
3. $13x^5+11x-6x^2+5$: The $x^2$ term comes after the $x$ term, so order is incorrect.
4. $7x^7+14x^9-17x+25$: The $x^9$ term (higher degree) comes after $x^7$, so order is incorrect.

Answer:

B. $12x^5 - 6x^2 - 9x + 12$