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. 8r2s4 â€"" 3r3s3 StartFraction 5 s Superscript 7 Baseline Over 6 EndFraction s5 3r4s5 â€""r4s6 â€""6rs5 StartFraction 4 r Over s Superscript 6 Baseline EndFraction.

Answer 1

Option C: $-6rs^5$

The last two terms given of the standard polynomial are:

$\cdots + 8r^2s^4 + 3r^3s^3$

This shows 2 patterns to us:

r 's degree is increasing per term in the given polynomial.

s 's degree is decreasing per term in the given polynomial.

The sum of powers of variates r and s is 2+4 = 3+3  = 6.

And since standard polynomial, the same pattern must be present in all terms of the series.

All options except C are not valid.

Option C has term $-6rs^5$ for which r's degree plus s's degree is 1 + 5 = 6.

And r's degree 1 <  s's degree 5.

Thus its a valid term to be putted as first term in standard form of polynomial in consideration.

Thus Option C: $-6rs^5$  is the needed expression.

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