2x³-3x+1/2x³+3x²-11x-6.what is the method to find its linear factors.

Hi,

The method goes like this. Look at the constant term first, one of the root is factor of 6, so +-1, +-2, +-3, +-6. One root is out of this and you have to check it. Now you have one root. If a is a root than x-a is a factor, divide the equation by x-a using long division method. You will get a quadratic as quotient. and we can easily factorize quadratic.

So x-a is one factor and two factor from quadratic. I.E. 3 factors.
It may happen that quadratic may not reduce into factors or the whole equation may have no roots.