Can someone explain how to Factor ... 1 + 8x^-1 + 15x^-2?

Answer 1

First factor out the smallest power of x:
(x^(-2))(x^2 + 8x + 15)
Then (x^(-2))(x + 3)(x + 5) is the answer.

Answer 2

1 + 8x^-1 + 15x^-2
= 1+8/x +15/x^2
= x^2/x^2 +8x/x^2 +15/x^2
= (x^2+8x+15)/x^2
= (x+5)(x+3)/ x^2

Answer 3

1 + 8x^-1 + 15x^-2

multiply with x^2/x^2

(x^2 + 8x + 15)/x^2

=>(1/x^2)[x^2 + 5x + 3x + 15)

=>(1/x^2)[x(x+5)+3(x+5)]

=>(1/x^2)[(x+5)(x+3)

=>[(x+5)(x+3)]/x^2

Answer 4

just fill in what you know.
you know both left sides have to be one
(1 + )(1 + )
and you know you need x^-1 on the right,
(1 + X^-1 )(1 + X^-1 )
Now all you need to do is find two numbers that sum to 8 and multiply to 15
Break it down into a chart:
1 15
3 5
Not much to choose from. 1+15 is sixteen, I hope 3+5 is 8, and I think it works. So you just fill in that for the number preceeding x,
(1 + 5X^-1 )(1 + 3X^-1 )
there ya go! I hope you understand how I got there, not the solution.
you can also put this into another form if you wish, but there is no need, I think that reciprocols are pretty simple.