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Factorisation- Trigonometric

f(t)= 2t^3 - t^2 - 13t - 6 = 0

and hence solve 2tan^3x = sec^2x +13tanx + 5
for -pi < x < pi

i've got (t + 3)(t-2) ((2t-3) +2t - 24

is this right??
Reply 1
Avatar for B_9710
B_9710
18
You should be able factorise f(t) into 3 linear factors.
Reply 2
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Tau
10
When you factorise a cubic, you shouldn't have an additional term or two added on the end: it should just be 3 brackets. Find a number k k such that f(k)=0 f(k) = 0 . From the factor theorem, (t−k) (t-k) is a factor of f(t) f(t) , so you can write your cubic as f(t)=(t−k)(at2+bt+c) f(t) = (t-k)(at^2 + bt + c) , and then you can equate coefficients to find a quadratic, and solve this quadratic to find the other factors of the cubic.

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