Christina S.

asked • 03/26/15

X^3-x^2-81x-81

Please factor.

Kevin C.

tutor
Are you sure this is copied correctly? Is it x3 - x2 - 81x + 81? If so, let x = -9 and use synthetic division to factor.
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03/26/15

Michael J.

You can also let x = 9, x = ± 3,  x = ±1 and use the method Kevin suggested.  If your remainder is zero when using division, then you will have your factors.  If not, try the next x-values as your divisor until you obtain a remainder of zero.
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03/27/15

Christina S.

Sorry, I guess I didn't explain properly.  My grandson is doing factoring and I am checking his work.  He has (x^2-81)(x+1), but I think it can Be factored further.  Also, not sure if +and - numbers are correct.  I would like to see the steps.  Thank you so much!
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03/27/15

Mark M.

tutor
(x2 - 81)(x + 1) = x3 + x2 - 81x - 81
 
x3 + x2 - 81x - 81 can be factored by grouping:
 
x3  + x2 - 81x - 81 = x2(x + 1) - 81(x + 1)
 
                          = (x + 1)(x2 - 81)
      
                          = (x = 1)(x - 9)(x + 9)
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03/27/15

Mark M.

tutor
Sorry, in my previous comment, "x = 1" should read x + 1.
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03/27/15

2 Answers By Expert Tutors

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Michael J. answered • 03/27/15

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(x2 - 81)(x + 1)
 
Notice that the term (x2 - 81) is a difference of perfect squares.  This is because when you square x, you get x2. When you square 9 or (-9), you get 81.  Also, the term is a difference since you have a minus sign. Knowing this, we can easily factor using the FOIL method.
 
(x - 9)(x + 9)
 
Therefore, when we factor the entire polynomial, we obtain
 
(x - 9)(x + 9)(x + 1)
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