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The degree of polynomial p is 11, and the degree of polynomial q is 7. Find all possible degrees of the polynomial p+q. Keep in mind that the degree can cancel out each other

 Apr 5, 2024

Best Answer 

 #2
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The only possible degree of p+q is 11.

No matter how you cancel out, you can't cancel out the coefficient of the ^11 term because the highest degree of q is 7. Because degree is defined by the highest exponent the degree is always 11.

 Apr 5, 2024
edited by hairyberry  Apr 5, 2024
 #1
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The degree of the polynomial p + q depends on the terms of both p and q. There are two main scenarios to consider:

 

No common factors: If p and q have no common factors (i.e., no variable raised to the same power in both polynomials), then the degree of p + q will simply be the larger of the two individual degrees.

 

In this case, p has a degree of 11 and q has a degree of 7. So, the degree of p + q would be 11.

 

Common factors: If p and q share some common factors (i.e., a variable raised to the same power appears in both), then the degree of p + q can be lower than the highest individual degree.

 

However, the degree can only be lowered by at most 1. This happens when the terms with the common factors cancel out when added together.

 

In this scenario, the possible degree of p + q would be between 10 (1 less than the highest degree) and 11.

 

Therefore, depending on the specific form of p and q, the possible degrees of the polynomial p + q are:

 

11: If there are no common factors between p and q.

 

10: If there is a common factor that cancels out upon addition.

 Apr 5, 2024
 #2
avatar+394 
+2
Best Answer

The only possible degree of p+q is 11.

No matter how you cancel out, you can't cancel out the coefficient of the ^11 term because the highest degree of q is 7. Because degree is defined by the highest exponent the degree is always 11.

hairyberry Apr 5, 2024
edited by hairyberry  Apr 5, 2024

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