Thread: im stuckk on polymonial equation.. need help!

So i was following the textbook with dividing the polynomial to find a quadratic factor..

the polynomial is 4x^3 -10x^2 -8x +6 =0
and i was dividing it by x-3 as it is a root of it.

I divided it and got the answer (x-3)(2x^2-4x-20)-54
What else do i need to do to it, to find the quadratic factor.. or to set it out right?

Need help!!!

Perform the long division algorithm . . . . if it is hard, resort to factoring.

you have to factor 4x^3 -10x^2 -8x +6;

Well, it factors to 2(x + 1)(2x - 1)(x - 3), that means if you factor (x - 3),

you are left with 2(x + 1)(2x - 1), right?

Then, 2(x + 1)(2x - 1) = 2(2x^2 + x - 1) = 4x^2 + 2x - 2.

Thus, (4x^3 -10x^2 -8x +6)/(x - 3) = (4x^2 + 2x - 2).
dividend divisor quotient