Determine a polynomial function of lowest degree with rational coefficients that has the roots 3+2i, 3-2i , -1 (multiplicity 2). Can someone help and exlain to me how to solve this?

Multiplicity 2 tells us that the root -1 occurs twice, so 


 

i.e. 


 


Therefore the least degree would be 4: 
 


:)

a) Find the number of terms and the degree of this polynomial.
b) Find the constant term and leading term.

Solution:
a)
This polynomial has 4 terms. Terms are separated by addition or subtraction. Its degree is 3, because 3 is the greatest value for an exponent for its terms

b)
The constant term is -32 and the leading term is -2

Add or subtract Polynimials

Solution:
We can simplify by combining the like terms. Like terms are the ones that are alike in every way except for maybe their coefficients. To simplify subtraction we can convert to addition (and eventually reverse the signs on every term of the subtrahend)