Question

Four polynomials are shown below: A. 3 − 7x5 + x2 B. 5x3 + 5 − 3x C. 3x + 2x3 − x2 + 6 + 2x D. 3x3 − 5 + 2x5 + x + 2x2 Which of the above polynomials is a 5th degree trinomial? Polynomial A Polynomial B Polynomial C Polynomial D

Answer 1

polynomials A and D are 5th degree polynomials

The degree of a polynomial is determined by the term with the largest exponent, given the polynomial in standard form

In A the term with the largest exponent is 7
`x^(5)`

In B the term is 5x³

In C the term is 2x³

In D the term is 2
`x^(5)`

A and D are polynomials of degree 5

B and C are polynomials of degree 3

Answer 2

A.
`3-7x^5 + x^2`

Explanation:

A 5th degree trinomial is the polynomial with three term and having degree 5.

Also, degree is the highest power of the monomial ( single term ) in the polynomial,

`5x^3 + 5 - 3x` having degree 3,

`3x+2x^3-x^2+6+2x` having degree 3,

So, they can not be the answer,

`3x^3 - 5 + 2x^5 + x + 2x^2` having degree 5 but it is not a trinomial,

Hence, only
`3-7x^5+x^2` is the trionomial having degree 5.

i.e. option A is correct.