19. If the polynomial P(x) = 27x^3 + 9x^2 – 3x – 10 is divided by 3x – 2, the remainder will be
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notice where how many "yes" sign change happen in the positive "x"
and the on the negative "-x"
for the P(x) is 3 changes, thus
so is either 3 real positive ones, or 3-2 = 1 real positive one
P(-x) gives no sign changes, so there are 0 negative ones
the polynomial has a degree of 5, thus 5 roots
if it has 3 real positive ones, then it has 2 complex ones
the complex ones pick up the slack per se
if it has 1 real positive one, then it has 4 complex ones
bear in mind complex ones always come in pairs