Asked by Logan
Factor the polynomial
X^3 + 8
X^3 + 8
Answers
Answered by
Scott
google "sum of cubes"
x^3 + 2^3
x^3 + 2^3
Answered by
Bosnian
To factor x³ + 8 you must use sum of cubes formula:
A³ + B³ = ( A + B ) ( A² - A ∙ B + B² )
In this case :
A = x
B = 2
becouse 2³ = 8
So:
x³ + 8 = x³ + 2³
x³ + 2³ = ( x + 2 ) ( x² - x ∙ 2 + 2² ) =
( x + 2 ) ( x² - 2 x + 4 )
x² - 2 x + 4 can't be factoring becouse discriminant of x² - 2 x + 4:
D = b² - 4 ∙ c = ( - 2 )² - 4 ∙ 1 ∙ 4 = 4 - 16 = - 12
This mean:
x² - 2 x + 4 has two complex solutions and can't be factoring with real numbers.
Solution:
x³ + 8 = ( x + 2 ) ( x² - 2 x + 4 )
A³ + B³ = ( A + B ) ( A² - A ∙ B + B² )
In this case :
A = x
B = 2
becouse 2³ = 8
So:
x³ + 8 = x³ + 2³
x³ + 2³ = ( x + 2 ) ( x² - x ∙ 2 + 2² ) =
( x + 2 ) ( x² - 2 x + 4 )
x² - 2 x + 4 can't be factoring becouse discriminant of x² - 2 x + 4:
D = b² - 4 ∙ c = ( - 2 )² - 4 ∙ 1 ∙ 4 = 4 - 16 = - 12
This mean:
x² - 2 x + 4 has two complex solutions and can't be factoring with real numbers.
Solution:
x³ + 8 = ( x + 2 ) ( x² - 2 x + 4 )
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.