Question

Help Please 15 points

Write each polynomial in standard form. 2x2 + x3 – 3 + 4x5

(a) 3 + 2x2 + x3 + 4x5

(b) 4x5 + x3 + 2x2 + 3

(c) 4x5 + x3 + 2x2 – 3

(d) 4x5 + 2x2 + x3 – 3

Answer 1

The Answer is c: 4x5 + x3 + 2x2 – 3

Explanation:

Answer 2

`4\,x^5+x^3+2x^2-3\\` which is option (c)

Explanation:

The standard form of a polynomial involves writing its terms in decreasing order of their degree. That is: the terms with larger degree are written first, and followed by the terms with lower degree.

In this case the terms of the polynomial are:

`2\,x^2\,,\, x^3\,,\,-3\,,\, and \, 4\,x^5`

Therefore, the term with largest degree (larger power of x) is
`4\,x^5` (its degree is "5" because the power in the variable x is 5)

the following term according to its degree should be:
`x^3` (its degree is "3" because the power in the variable x is 3)

the next one is
`2\,x^2` (its degree is "2" because the power in the variable x is 2)

the last term is the constant term "-3" (with degree zero since the variable x does not appear in it)

Therefore the standard form of the polynomial comes from rearranging the terms in decreasing order of their degrees as:

`4\,x^5+x^3+2x^2-3\\`