SOLUTION: Are both x^2+16 and x^3+27 factorable? Why or why not (explain).

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Are both x^2+16 and x^3+27 factorable? Why or why not (explain).      Log On


   

Question 1133459: Are both x^2+16 and x^3+27 factorable? Why or why not (explain).
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2B16
x%5E2-%28-16%29
x%5E2-%28-1%29%284%5E2%29
x%5E2-%284i%29%5E2
%28x%2B4i%29%28x-4i%29
If you allow imaginary numbers, then your given quadratic expression is factorable.


You can decide about your cubic expression on your own. Try polynomial division with divisors of x+3 and x-3, and see what happens.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Are both x^2+16 and x^3+27 factorable? Why or why not (explain).
Sum of squares(matrix%281%2C3%2C+x%5E2+%2B+16%2C+or%2C+%28x%29%5E2+%2B+%284%29%5E2%29) CANNOT be factored with INTEGERS. 

x%5E3+%2B+27 follows the SUM OF CUBES method of factoring, or matrix%281%2C3%2C+a%5E3+%2B+b%5E3%2C+%22=%22%2C+%28a+%2B+b%29%28a%5E2+-+ab+%2B+b%5E2%29%29, to factor to: highlight_green%28%28x+%2B+3%29%28x%5E2+-+3x+%2B+9%29%29