Factoring A Polynomial With A Negative Exponent

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spaceshowfeature1

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Use the knowledge of factoring you've gained to factor this problem: x^2+1-6x^-2. I start by choosing my GCF as x^-2 or 1/x^2. I then tried to divide each term by x^-2, and I get x^-2(x^2-x^-2-6x^2). This is horribly wrong, as the answer according to https://www.emathhelp.net/calculato...olynomials-calculator/?p=x^2+1-6x^-2&steps=on is 1/x^2(x^2-2)(x^2+3). What do I need to do to get the answer correct? If you need more information, just ask! :D
 
x^2 + 1 - 6x^-2 = x^2 +1 - 6/x^2
Multiply by x^2 : (x^4 + x^2 - 6) / x^2

OK?

Given answer is correct...
 
spaceshowfeature1 said:
Use the knowledge of factoring you've gained to factor this problem: x^2+1-6x^-2. I start by choosing my GCF as x^-2 or 1/x^2. I then tried to divide each term by x^-2, and I get x^-2(x^2-x^-2-6x^2). This is horribly wrong, as the answer according to https://www.emathhelp.net/calculato...olynomials-calculator/?p=x^2+1-6x^-2&steps=on is 1/x^2(x^2-2)(x^2+3). What do I need to do to get the answer correct? If you need more information, just ask! :D
Click to expand...

As has been said, the way to divide by x^-2 is to multiply by its reciprocal, x^2. I'm not sure what you did, but probably the negative got you.

Whenever I factor anything, I check it; that can tell me if I'm wrong, and often show me where. In this case, multiplying gives us

x^-2(x^2 - x^-2 - 6x^2) = x^-2(x^2) - x^-2(x^-2) - x^-2(6x^2) = 1 - x^-4 - 6
​

which is clearly wrong.

After doing the correct multiplication, you can factor the result.

A few quibbles: what you are factoring is not a "problem" but an expression; and it's a good idea to use parentheses when you combine division with multiplication, so the answer is (1/x^2)(x^2-2)(x^2+3), or (x^2 - 2)(x^2 + 3)/x^2. That helps clarify what you mean.
 
Dr.Peterson said:
As has been said, the way to divide by x^-2 is to multiply by its reciprocal, x^2. I'm not sure what you did, but probably the negative got you.

Whenever I factor anything, I check it; that can tell me if I'm wrong, and often show me where. In this case, multiplying gives us
x^-2(x^2 - x^-2 - 6x^2) = x^-2(x^2) - x^-2(x^-2) - x^-2(6x^2) = 1 - x^-4 - 6
​

which is clearly wrong.

After doing the correct multiplication, you can factor the result.

A few quibbles: what you are factoring is not a "problem" but an expression; and it's a good idea to use parentheses when you combine division with multiplication, so the answer is (1/x^2)(x^2-2)(x^2+3), or (x^2 - 2)(x^2 + 3)/x^2. That helps clarify what you mean.
Click to expand...
Thanks. The negative defiantly got me!
 
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