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Cubic equation

I am trying to solve this cubic equation and have only one solution and I can't find the others.
X^3+ - 24x + 32 =0
Using a the factor theorem I have worked out one solution:x= 4
This equation doesn't divide using polynomial long division as it does not have an x^2term
I would really appreciate it if some one could give me another solution and could explain the method used
Thanks in advance
Just because it doesn't have an x^2 term doesn't mean you can't divide.

Even so, the 'forming the cubic' method is generally superior in my opinion as it takes a lot less time.

x^3-24x+32 = (x-4)(x^2+4x-8)

Then find the roots of x^2+4x-8
You can't factorise it, but by completing the square you get (x+2)^2 = 12
x = -2+-root12
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123_qwerty
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Thank you, but how did you work out the quadratic
Original post by 123_qwerty
I am trying to solve this cubic equation and have only one solution and I can't find the others.
X^3+ - 24x + 32 =0
Using a the factor theorem I have worked out one solution:x= 4
This equation doesn't divide using polynomial long division as it does not have an x^2term
I would really appreciate it if some one could give me another solution and could explain the method used
Thanks in advance


Writing x3+0x2−24x+32x^3 + 0x^2 - 24x + 32 will solve your division problem.

Alternatively call the quadratic Ax2+Bx+CAx^2+Bx+C and equate coefficients.

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