Question 1038373: Tell how to factor a polynomial with four terms (that you choose) by grouping.
Answer by addingup(3677)   (Show Source):
You can put this solution on YOUR website! I'll factor:
x^3+x^2–x–1
Break into two groups
(x^3+x^2)+(–x– 1)
Now find the GFC of each of those two sets and factor out:
x^2 is the GCF of the first set, and –1 is the GCF of the second set. Factoring out both of them, you get x^2(x+1)–1(x+1)
And we factor again, since the two terms we now have both have a GFC of x+1:
(x+1)(x^2–1)
So, what do we have now. We have x^2-1 is a difference of squares and factors again as (x+1)(x-1). This gives you a final factorization of: (x+1)(x+1)(x–1), or (x+1)^2(x–1)
Final note: Once you start factoring, you may end up at a dead end because the polynomial may end up being prime. And that's OK, when you reach the end you reach the end.
John
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