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PilotLPTM [1.2K]
3 years ago
11

If x+3 is one factor of x^3 +27 what is the other factor

Mathematics
2 answers:
levacccp [35]3 years ago
6 0

Work is provided in the image attached.

kenny6666 [7]3 years ago
3 0
For this case we have the following third degree polynomial:
 x ^ 3 +27

 By completely factoring the polynomial we have:
 (x + 3) (x ^ 2 - 3x + 9)

 We will verify that the factorization is correct.
 For this, we make distributive property:
 (x ^ 3 - 3x ^ 2 + 9x) + (3x ^ 2 - 9x + 27)

 We add similar terms:
 x ^ 3 + (-3x ^ 2 + 3x ^ 2) + (9x - 9x) + 27

x ^ 3 +27
 Therefore, the factorization is correct.
 So, the other factor is:
 (x ^ 2 - 3x + 9)
 Answer:
 
the other factor is:
 
(x ^ 2 - 3x + 9)
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