Question

Which terms could be used as the first term of the expression below to create a polynomial written in standard form? Select five options.

[ + Br^5 - 31s^2 - 5s + 3435 - rs + 0.655r^4 ]
a. ( Br^5 )
b. ( -31s^2 )
c. ( 5s )
d. ( 3435 )
e. ( -rs )

Answer 1

The terms (Br^5) and (0.655r^4) can be used as the first term in the expression to create a polynomial in standard form since they have the highest degrees of the given variable 'r'. The terms (-rs), (-31s^2), and (5s) could follow respectively as they contain variables 'r' and 's' but have lower degrees than (Br^5).

Step-by-step explanation:

To create a polynomial in standard form, the terms must be ordered from highest to lowest degree based on the variable's exponents. The given expression is [ + Br^5 - 31s^2 - 5s + 3435 - rs + 0.655r^4 ]. When selecting the term that could be the first in the expression to achieve standard form, we should choose the term with the highest degree. Let's evaluate the available options:

• (Br^5): This term has the highest degree (r^5) and hence, can be used as the first term in standard form.
• (-rs): This term has degree 1 when considering both r and s, which is lower than (Br^5) and should not be the first term.
• (-31s^2), (5s), and (3435): These terms involve a different variable, 's,' and their degrees are lower compared to (Br^5).
• (0.655r^4): This term's degree (r^4) is lower than (Br^5) but is still a potential candidate since it involves the same variable, 'r'.

Considering this, the terms that can be used as the first term to create a polynomial written in standard form from the given options are:

1. (Br^5)
2. (0.655r^4)
3. (-rs)
4. (-31s^2)
5. (5s)