1. The problem statement, all variables and given/known data First find all rational zeros of f, then use the depressed equation to find all roots of the equation f(x) = 0. f(x) = x^3 + 5x^2 - 8x + 2 2. Relevant equations 3. The attempt at a solution Possible rational zeros: 2, -2, 1, -1 Synthetic division: 1 | 1 5 -8 2 _____1 6 -2 ============= 1 6 -2 0 Quotient: x^2 + 6x - 2 Factored: (x + 3)^2 - 11 I would think that the answer would just be x = -3 ± √(11) but the answer in the book says: {1, -3 ± √(11)} Where'd the 1 come from?
Remember, you divided by (x-1), so your equation become (x-1)(x^2+6x-2)=0 -> x= 1 in addition to the other roots you found.
synthetic division, oh lord if you want a nicer division algorithm try this or proper polynomial long division ... I really hated synthetic division :p
I believe we've had this discussion before, but there's nothing wrong with synthetic division. It's quick and pretty straightforward, IMO. Of course, if you're trying to divide a polynomial by a quadratic or a higher degree polynomial, then long division is the way to go.