Use use the rational zero theorem to solve 21x^6+32x^5-180x^4+130x^3+55x^2-66x+8

Question

I used synthetic division and got it down to 21x^4-31x^3-3x^2+15x-2 and I'm not sure where to go from there. How would I plug that into the quadratic formula to get the remaining zeros.

Answer 1

21x^4 -31x^3 -3x^2 + 15x -2 = 0 when x=1

21-31 -3 +15 -2

= 36-36 = 0 x-1 is a factor, divide the 4th degree polynomial by x-1 or use synthetic division to get

21x^3 -10x^2 -17x -2