Respuesta :
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.
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.
The terms that could be used as the first term of the given polynomial expression to create a polynomial written in standard form are;
Option B; 3r⁴s⁵
Option C; -r⁴s⁶
Option D; -6rs⁵
The options are;
A) s⁵
B) 3r⁴s⁵
C) -r⁴s⁶
D) -6rs⁵
We are given the polynomial expression;
+8r²s⁴ - 3r³s³
Now, the two terms of the given polynomial will each have a degree of 6. This is because the sum of their exponents is the degree;
For +8r²s⁴, we add the exponents to get 2 + 4 = 6
Also for 3r³s³, we add the exponents to get 3 + 3 = 6
This means that for any term that will start the polynomial must have a degree greater than 6.
Option A; s⁵ cannot start the polynomial because it has a degree of 5 which is less than 6.
Option B; 3r⁴s⁵ can start the polynomial because it has a degree of 4 + 5 = 9.
Option C; -r⁴s⁶ can start the polynomial because it has a degree of 4 + 6 = 10.
Option D; The degree of -6rs⁵ is 6 but it can also start the polynomial because the exponent of s is greater than the other two in the given expression.
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