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What is the factor of X cube minus 27?
Algebra Examples Rewrite 27 as 33 . Since both terms are perfect cubes, factor using the difference of cubes formula, a3−b3=(a−b)(a2+ab+b2) a 3 – b 3 = ( a – b ) ( a 2 + a b + b 2 ) where a=x and b=3 .
Which of the following expressions are the factors of 27?
Factors of 27
- Factors of 27: 1, 3, 9 and 27.
- Negative Factors of 27: -1, -3, -9 and -27.
- Prime Factors of 27: 3.
- Prime Factorization of 27: 3 × 3 × 3 = 33
- Sum of Factors of 27: 40.
How do you solve x cubed plus 27?
Example: Factor x 3 + 27.
- Think of 27 as 3 3. Then this is a sum of cubes and we can apply the sum of cubes formula: a 3 + b 3 = (a + b) (a 2 − a b + b 2 ).
- Substituting a = x and b = 3 into the formula yields: x 3 + 27 = (x + 3) (x 2 − 3 x + 9).
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What is the perfect cube root of 27 = 33?
Both x3 and 27 = 33 are perfect cubes. So we can use the difference of cubes identity: with a = x and b = 3 as follows: This is as far as you can go with Real coefficients. If you allow Complex coefficients then you can factor this a little further: where ω = − 1 2 + √3 2 i is the primitive Complex cube root of 1.
How do you find the perfect cube of X3?
Use the difference of cubes identity to find: Both x3 and 27 = 33 are perfect cubes. So we can use the difference of cubes identity: with a = x and b = 3 as follows: This is as far as you can go with Real coefficients. If you allow Complex coefficients then you can factor this a little further: