Consider the polynomial p(x)=32x5y−2xy5.
Part A: What is the complete factorization of p(x)=32x5y−2xy5 over the integers?
Part B: What methods are used to factor p(x)=32x^5y−2xy^5?
Select one answer for Part A and select all answers that apply for Part B.
B: greatest common factor
A: 2xy(2x−y)(2x+y)(4x2+y2)
B: difference of cubes
B: grouping
A: 2xy(4x2−y2)(x4−4x2y2+y4)
B: repeated difference of squares
A: 2xy(2x−y)2(2x+y)2
My answer
A: 2xy(2x−y)(2x+y)(4x2+y2)
B: repeated difference of squares
correct
Your answer is correct!
Part A: The complete factorization of the polynomial p(x) = 32x^5y - 2xy^5 over the integers is 2xy(2x−y)(2x+y)(4x^2+y^2).
Part B: The methods used to factor p(x) = 32x^5y - 2xy^5 are:
- Repeated difference of squares: This method is used to factor out common factors by recognizing the form a^2 - b^2. In this case, we can rewrite 4x^2 - y^2 as (2x)^2 - y^2, which is in the form of a difference of squares.
Therefore, we can factor 32x^5y - 2xy^5 as 2xy(2x−y)(2x+y)(4x^2+y^2).
Well done!