# SOLUTION: x^3 + 5x^2 + 8x + 6 = 0 solve with horner method plz

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 Click here to see ALL problems on Polynomials-and-rational-expressions Question 762798: x^3 + 5x^2 + 8x + 6 = 0 solve with horner method plz Answer by Edwin McCravy(13211)   (Show Source): You can put this solution on YOUR website! ```Horner's method is simply synthetic division. x³ + 5x² + 8x + 6 = 0 The feasible rational roots are ± the factors of 6, which are ±1, ±2, ±3, ±6 It has no sign changes (all terms positive), so there are no positive roots. So we need try only negative feasible rational roots: We try -1 -1|1 5 8 6 | -1 -4 -4 1 4 4 2 No, that doesn't give 0 on the far right. We try -2 -2|1 5 8 6 | -2 -6 -4 1 3 2 2 No, that doesn't give 0 on the far right, either. We try -3 -3|1 5 8 6 | -3 -6 -6 1 2 2 0 Whoopie do! That give 0 on the far right! So we have have found one zero -3. The above synthetic division is a shortcut for long division of dividing by (x + 3) and getting x² + 2x + 2 as a quotient, so we have now factored: x³ + 5x² + 8x + 6 = 0 as (x + 3)(x² + 2x + 2) = 0 Using the zero factor principle: x + 3 = 0; x² + 2x + 2 = 0 x = -3 x = x = x = x = x = x = x = x = -1 ± i So the three roots are -3, -1 + i, -1 - i Edwin```