Ok heres another factoring that I need someone to check
Problem: -x^3 + 27
-(x^3 - 3^3)
So I moved the positive and found out what cubed would make 27
Using the forumla: (a-b)(a^2+ab+b^2)
-(x-3) (x^2 + 3x + 9)
Right? Or did I make a mistake?
That is correct, you can always double check your answer by expanding it
-(x^3+3x^2+9x-3x^2-9x-27)
cancel the ones you need to cancel and you get
-(x^3-27)
=-x^3+27
So I factored it right? Ha thanks alot.
To check if your factoring is correct, let's expand the expression (-x + 3)(x^2 + 3x + 9) and see if it simplifies back to the original expression -x^3 + 27.
When we multiply the expressions, we get:
(-x + 3)(x^2 + 3x + 9) = -x(x^2 + 3x + 9) + 3(x^2 + 3x + 9)
= -x^3 - 3x^2 - 9x + 3x^2 + 9x + 27
= -x^3 + 27
So, your factoring is indeed correct:
-x^3 + 27 = -(x - 3)(x^2 + 3x + 9)
Well done!