Math help - factorising cubic equations

Using the integer root and factor theorem, solve:
18x^3 + 54x^2 + 40x + 8 = 0

(The ^ symbol means it is squared.)

I got one of the x's and got (x+2) as one of the factors, but beyond that, I'm having trouble finding the other two.

Reply 1

mqb2766

Original post by Nice_100

"divide" the cubic by that factor to get the other quadratic, then the two other factors should be clear? Generally dividing means compare coefficients so
(x+2)(ax^2+bx+c) = 18x^3 + 54x^2 + 40x + 8
and get a,b,c. You could divide by 18 at the start and note the product of the roots is 4/9, so if one is 2 then the product of the other two is 2/9.

(edited 6 months ago)

Reply 2

username6520364

Alternatively, you could expand this (x+2)(ax^2+bx+c) and note that it's equivalent to 18x^3 + 54x^2 + 40x + 8.
That would allow you to find a, b and c before factorising it like a normal quadratic. I'd assume mqb2766's methods quicker, but perhaps this inverse method is more intuitive.