factorise the following using the factor theorem (1) X cube-3x square-9x+5 (2) x cube -3x square+13xsquare +32x+20
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By a direct checking
f(5) = 0 where f(x) = x^3 - 3x^2 - 9x - 5.
Thus, f(x) = x^2(x- 5) + 2x(x - 5) + (x - 5)
= (x-5)( x^2 + 2x + 1)
= (x-5)(x + 1)^2.
One can also check that f(-1) = 0 & proceed accordingly.
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