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3 years ago

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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