Question

solve 3x^3+x^2-8x+4>0. show all the algebraic calculations. (5 marks) (for grade 12 ways)

Answer 1

first try, x=1, turns out to be a zero

So ... synthetic division
3x^3+x^2-8x+4 > 0
(x-1)(3x^2 + 4x - 4) > 0
(x-1)(x+2)(3x - 2) > 0

so the corresponding function y = 3x^3 + x^2 - 8x + 4
has x-intercepts of -2, 1 and 2/3
and knowing the shape of this standard cubic to open upwards into the first quadrant
the given inequation will be positive for
-2 < x < 2/3 OR x > 1

picture of your problem:
http://www.wolframalpha.com/input/?i=3x%5E3%2Bx%5E2-8x%2B4%3D0