Answer:
3r⁴s⁵
- r⁴s⁶
- 6rs⁵
Step-by-step explanation:
1) The expression given is:
+ 8r²s⁴ – 3r³s³
2) The choices given are:
s⁵
3r⁴s⁵
- r⁴s⁶
- 6rs⁵
1) A polynomial written in standard form has the terms ordered in decreasing order.
For example, 4x⁵ + 8x⁴ + 3x² + 27
2) The given polynomial has degree 6: + 8r²s⁴ – 3r³s³, and it can be ordered respect any of the two variables either r or s.
3) Adding a new term as first term needs to have degree equal or greater than 6.
So, the candidates from the list are: 3r⁴s⁵, - r⁴s⁶,- 6rs⁵
4) If you use 3r⁴s⁵, the polynomial in standard form would be:
3r⁴s⁵ – 3r³s³ + 8r²s⁴ (as you see the degree of r is decreasing from left to right).
5) If you use - r⁴s⁶, the polynomial in standard form would be:
- r⁴s⁶ – 3r³s³ + 8r²s⁴ (as you see, the degree of r decreases from left to right)
6) If you use - 6rs⁵, the polynomial in standard form would be
- 6 rs⁵– 3r³s³ + 8r²s⁴ (as you see the degree of s is decreasing from left to right).
7) You cannot use s⁵ as first term because its degree is less than 6.
