Question

Express the polynomial 5a^2+3a^3+1 in standard form and then classify it

A. Quadratic monomial
B. Linear monoimal
C. Cubic binomial
D. Cubic trinomial

Answer 1

For this case we have that by definition, the standard form of a polynomial is given by:

`P(x)=ax^n+bx^(n-1)+ ... +cx^3+ dx^2+ ex +f`

Where:

`n, n-1,3,2,1`: Are the exponents

x: It is the variable

a, b, c, d, e: Are the coefficients

f: It is the independent term

n: It is the degree of the polynomial (greatest exponent)

In this case we have the following expression:

`5a^2+3a^3+1`

We express in the standard way:

`3a^3+5a^2+1`

It is noted that the polynomial has 3 terms, so it is a trinomial. In addition, the greatest exponent is "3" (so 3 is the degree of the trinomial), so we have that it is a cubic trinomial.

Answer:

OPTION D