Q:

# Which terms could be used as the first term of the expression below to create a polynomial written in standard form? Check all that apply. + 8r2s4 – 3r3s3 s5 3r4s5 –r4s6 –6rs5

Accepted Solution

A:
Answer:

3r⁴s⁵
- r⁴s⁶

- 6rs⁵

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.