use factor theorem to factorise 6 x cube + 17 X square + 44 X - 12 completely give me the answer please
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Answer: Let f(x) = 6x³+17x²+4x-12
Factors of the constant term (12) : +-1,+-2,+-3,+-4,+-6,+-12
By hit and trial method,
f(-1) = 6(-1)³+17(-1)²+4(-1)-12
= -6+17-4-12
= -5 (not equal to 0)
Therefore, x+1 is not a factor of f(x).
f(-2) = 6(-2)³+17(-2)²+4(-2)-12
= 6(-8)+17(4)+(-8)-12
= -48+68-8-12
= 68-68
= 0
Therefore, x+2 is a factor of f(x).
By long division method, we get 6x²+5x-6.
By middle term splitting,
6x²+5x-6
= 6x²+9x-4x-6
= 3x(2x+3) - 2(2x+3)
= (2x+3)(3x-2) are the other two factors of f(x).
Therefore, the factories of f(x) are (x+2), (2x+3) and (3x-2).
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