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By inspection, the sum of the coefficients is 1 - 5 + 4 = 0Therefore x = 1 is a root. That is (x - 1) is a factor.
Then suppose the other factor is ax^2 + bx + c
SInce the coefficient of x^3 is 1, then a = 1 so that the second factor is x^2 + bx + c
Therefore (x - 1)*(x^2 + bx + c) = x^3 - 5x + 4
x^3 - x^2 + bx^2 - bx + cx - c = x^3 - 5x + 4
Comparing coefficient of x^2 gives -1 + b = 0 so that b = 1
Comparing coefficient of x gives -b + c = -5 so that c = b - 5 = -4
Comparing constant terms gives -c = 4 or c = -4 which confirms above calculations.
Thus, the second factor is (x^2 + x - 4) which does not have rational factors.
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the answer is (3x-2)(9x squared+6x+4)
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n(2n - 1)(2n + 7)
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(x - 2)(2x - 3)
