1.)The polynomial 729 x^{3} - 1 y^{3} can be factored into the product of two polynomials, A * B where the degree of A is greater than the degree of B. Find A and B.

Question

2.)The polynomial 16 a^{6} + 8 a^{3}b + 1 b^2 - 49 c^{6} can be factored into the product of two polynomials, A * B where the coefficient of c in A is less than the coefficient of c in B. Find A and B.

Answer 1

strange wording for a problem that simply could be stated as ...

factor 729x^3 - y^3

then
729x^3 - y^3 = (9x-y)(81x^2 + 9xy + y^2)

so I guess
B is 9x-y and
A is 81x^2 + 9xy + y^2

For the second, I will simply factor it, ignoring the strange conditions.

16a^6 + 8a^2b + b^2 - 49c^6
= (4a^2+b)^2 - 49c^6 , a difference of squares
= (4a^2 + b + 7c^3)(4a^2 + b - 7c^3)

Answer 2

wow thank you so much! i spent hours on that problem. thanks again for the help.

Answer 3

I am just curious who is giving you such unusually phrased questions.
Are these from your textbook ?

Answer 4

It's from a website called WebWork where we do the homework on.