Help me with this word problem please!!!

Question

Janie writes a polynomial expression using only one variable x with a degree of 3. Max writes a polynomial expression using only one variable x with the degree of 7. What can you determine about the degree of the sum of Janie and max's polynomials? What can you determine about the degree of the difference of Janie and max's polynomials?

Answer 1

The degree of your resultant polynomial (no matter they are added or subtracted) is 7. When you are performing your operations with polynomials of different degrees you are combining only like terms (terms with the same degree). The degree of your resultant polynomial is the same like of the polynomial with the highest degree. If degrees of both polynomials are equal and with equal coefficients, then their subtraction will lower the degree of the resultant polynomial.

Answer 2

Degrees refer to the highest power in a polynomial when the polynomial is written in its simplest form. Janie writes a polynomial with one variable with a degree of 3, so the highest power in her polynomial is x³. We can write a very simplified version of her polynomial like this:

 

x³ + ...

 

Where the (...) just means any other things that can be included in a polynomial, so long as they only include the variable x and do not have a power higher than 3.

 

In the same sense, we can do the same with Max's polynomial, with only one variable x and power of 7:

 

x⁷ + ...

 

If we were to sum the two, we would get:

 

x⁷ + ... + x³ + ...

 

So the sum would have a degree of 7.

 

If we were to subtract the two:

 

x⁷ + ... - x³ + ...

 

It would still have a degree of 7.