How do you write a polynomial in standard form, then classify it by degree and number of terms #3a^3b – 4ab^2 + a2 #?

Question

How do you write a polynomial in standard form, then classify it by degree and number of terms  #3a^3b – 4ab^2 + a2 #?

Hazel Anglin · Accepted Answer

#3a^3 b - 4ab^2 + a2# should be arranged as it already is.
The "degree" of the first term is #4#.
The degree of the second term is 3, and the last one is 1 (#2a^1#).

"Standard Form" for a polynomial puts the highest exponent terms first, with the other in decreasing order. The "degree" is the level of the highest exponent power. Multiple exponent levels on one term are added. #3a^3 b - 4ab^2 + a2# should be arranged as it already is, with the #a^3# term having the highest exponent. The "degree" of the first term is the sum of both exponents, #3 + 1 = 4#. The degree of the second term is 3, and the last one is 1 (#2a^1#). https://tutor.hix.ai https://tutor.hix.ai

Hazel Anglin · Answer

undefined To write a polynomial in standard form, arrange the terms in descending order of degree and combine like terms. The given polynomial in standard form is: $3a^3b - 4ab^2 + a^2$.

The degree of a polynomial is determined by the highest exponent present. In this polynomial, the highest exponent is $3$, so it is a cubic polynomial.

The number of terms in a polynomial is the count of separate parts separated by addition or subtraction signs. In this polynomial, there are $3$ terms.