Question 667406: how to factor ax^3+a
i factored out the "a" and have
a(x^3+1)
i'm using (a+b) (a^2-ab+b^2)
i believe it's (x+1)(x^2-1x+1)
I'm stuck i don't know how to move on from here.
Thank you :)
Found 2 solutions by lynnlo, Alan3354:
Answer by lynnlo(4176)   (Show Source):
You can put this solution on YOUR website! ax^3+a
a(x^3+1)=0============solve for x
x^3+1=0===divide both sides by a constant to simplify the equation
(x+1)(x^2-x+1)=0===factor the left hand side
x+1=0 OR x^2-x+1=0=====split into 2 equations
look at the first equation,solve for X,subtract 1 from both sides
x=1 OR x^2-x+1=0
look at the second equation,solve the quadratic equation
by completing the square,subtract 1 from both sides x=-1 OR x^2-x=-1
add 1/4 to both sides======x=-1 OR x^2-x+1/4=-3/4
factor left side,write left hand side as a square=x=-1 OR (x-1/2)^2=-3/4
eliminate the exponent on left side,square root of both sides
x=-1 OR x-1/2= i√3/2 OR x-1/2=-1/2(i√3)
look at the second equation,solve for X,add 1/2 to both sides
x=-1 OR x=1/2+i√3/2 OR x-1/2=-1/2(i√3)
look at third equation,solve for X
add 1/2 to both sides
x=-1 OR x=1/2+i√3/2 OR x=1/2-i√3/2
Answer by Alan3354(69443)  (Show Source):
|
|
|
