SOLUTION: factor the polynomials using whatever strategy seems appropriate. State what methods you will use and then demonstrate the methods on your problems, explaining the process as you

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: factor the polynomials using whatever strategy seems appropriate. State what methods you will use and then demonstrate the methods on your problems, explaining the process as you       Log On


   



Question 788072: factor the polynomials using whatever strategy seems appropriate. State what methods you will use and then demonstrate the methods on your problems, explaining the process as you go. Discuss any particular challenges those particular polynomials posed for the factoring.
6w^4-54W^2 these are two separate problems 1-XY-20^2Y^2

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
6w%5E4-54w%5E2
The coefficients are both multiples of 6, because -54=6%2A%28-9%29, so we could take out 6 as a common factor.
Both terms have powers of w, and the smallest exponent is 2, and we can write w%5E4 as w%5E2%2Aw%5E2=w%5E4, so we could take out w%5E2 as a common factor.
We can take out both actors at the same time, as 6w%5E2
6w%5E4=6w%5E2%2Aw%5E2 and -54w%5E2=6W%5E2%2A%28-9%29
6w%5E4-54w%5E2=6w%5E2%28w%5E2-9%29
Next, we realize that w%5E2-9 is a difference of squares, a special product of the form
a%5E2-b%5E2=%28a%2Bb%29%28a-b%29.
Specifically, w%5E2-9=%28w%2B3%29%28w-3%29.
So the complete factorization is
6w%5E4-54w%5E2=6w%5E2%28w%5E2-9%29=highlight%286w%5E2%28w%2B3%29%28w-3%29%29