How do you write a polynomial in standard form, then classify it by degree and number of terms #6a^4 + 9a^3 - 12a^2#?

Question

Nathan Axel · Accepted Answer

#6a^4 + 9a^3 - 12a^2# is in standard form with degree of polynomial 4. It has three terms with #x^2# and constant terms having #0# coefficient.

Definition: A polynomial is in standard form when its term of highest degree is first, its term of 2nd highest is 2nd etc.. Examples of Polynomials in Standard Form. -# x^2 + x + 3# Non-Examples of Polynomials in Standard Form. #2y ^4 + 3y ^5 + 2+ 7# In the given sum #6a^4 + 9a^3 - 12a^2# is in standard form with degree of polynomial 4. It has three terms with #x^2# and constant terms having #0# coefficient.

Kennedy Adams · Answer

undefined To write a polynomial in standard form, arrange the terms in descending order of their exponents.

The given polynomial is $6a^4 + 9a^3 - 12a^2$. Rearranging the terms gives $6a^4 + 9a^3 - 12a^2$.

Next, classify the polynomial by degree and number of terms:

- Degree: The highest exponent in the polynomial is 4, so the degree of the polynomial is 4.
- Number of terms: There are three terms in the polynomial, so it is classified as a trinomial.