SOLUTION: The polynomial 49a^6−28a^3b+4b^2−4c^−4 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

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The polynomial 49a^6−28a^3b+4b^2−4c^−4 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      Log On


   

Question 1185497: The polynomial 49a^6−28a^3b+4b^2−4c^−4 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.
The numbers after '^' are exponents (6,3,2,-4)
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52903) About Me  (Show Source):
You can put this solution on YOUR website!
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The polynomial 49a^6−28a^3b+4b^2−4c^−4 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.
The numbers after '^' are exponents (6,3,2,-4)
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Hello, the long formula in your post is not a polynomial.


If you think it is a polynomial, it means that your eyes deceive you.



Answer by greenestamps(13215) About Me  (Show Source):
You can put this solution on YOUR website!


Your expression is

49a%5E6-28a%5E3b%2B4b%5E2-4c%5E%28-4%29

It is not a polynomial, because polynomials can't have negative exponents.

However, the expression is factorable using the pattern P^2-Q^2=(P+Q)(P-Q).

49a%5E6-28a%5E3b%2B4b%5E2-4c%5E%28-4%29

%2849a%5E6-28a%5E3b%2B4b%5E2%29-%284c%5E%28-4%29%29

%287a%5E3-2b%29%5E2-%28%282c%5E%28-2%29%29%5E2%29

%28%287a%5E3-2b%29%2B2c%5E%28-2%29%29%28%287a%5E3-2b%29-2c%5E%28-2%29%29

%287a%5E3-2b%2B2c%5E%28-2%29%29%287a%5E3-2b-2c%5E%28-2%29%29

Note that the two factors are also not polynomials, since they both contain negative exponents.