Use the factor theorem to show that (x-1) is a factor of x^3 - 3x^2 -13x + 15
If (x-1) is a factor of x3 - 3x2 -13x + 15 then one of the solutions for x must be x = 1.(This is because, if (x-1) is a factor of this equation then it is true that x-1=0, because this is a point where the curve crosses the x axis and therefore is = to 0. Solving x-1=0 gives x=1)Because we know that if (x-1) is a factor of the curve, the equation must equal 0 when x=1, we can just substitute this in as such:(1)3 - 3(1)2 -13(1) + 15= 1 - 3 - 13 + 15= 16 -16 = 0Therefore we can conclude, using the factor theorem that (x-1) is a factor of x3 - 3x2 -13x + 15
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