The equation x2 - 5x - 24 = 0 has the two solutions 8 and -3 for x.
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x2 - 5x = 0Factor the left side:x (x - 5) = 0x = 0x = 5
(x + 2)(x - 4)
f(x) = 3x2 + 5x + 2fprime(x) = 6x + 5
Provided that x- 2 is not zero: 2x3 + x2 - 13x + 6 = 2x3 - 4x2 + 5x2 - 10x - 3x + 6 = 2x2*(x - 2) + 5x*(x - 2) - 3*(x - 2) = (x - 2)*(2x2 + 5x - 3) Therefore, (2x3 + x2 - 13x + 6)/(x - 2) = (x - 2)*(2x2 + 5x - 3)/(x - 2) = 2x2 + 5x - 3 If x = 2 so that x - 2 = 0, then the expression is not defined.
x(x - 2)