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How do you factorise x3 - 27?

Updated: 4/28/2022
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14y ago

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-24

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Mohamed Purdy

Lvl 10
3y ago
This answer is:
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14y ago

it will be 3(x-27).

(provided that x3 means x*3).

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Q: How do you factorise x3 - 27?
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How would you factor x3 9x2 27x 27?

x3 + 9x2 + 27x + 27 Given the numbers in the equation, we can likely bet on (x + 3) being a factor. Let's try it with artificial division: 3 * 1 = 3 9 - 3 = 6 3 * 6 = 18 27 - 18 = 9 3 * 9 = 27 27 - 27 = 0 Bingo. So let's carry it out in long division:                       x2 + 6x + 9                    _____________________ x + 3 ) x3 + 9x2 + 27x + 27                        x3 + 3x2                                        6x2 + 27x                                        6x2 + 18x                                                                9x + 27                                                                9x + 27                                                                                    0 So we have: x3 + 9x2 + 27x + 27 = (x + 3)(x2 + 6x + 9) Which we can now factor further with relative ease: = (x + 3)(x + 3)(x + 3) = (x + 3)3