Question

factorise x3-x2-14x+24 by using factor theorem

Answer 1

Dear student
$$\begin{gathered} Letf\left(x\right)=x^3-x^2-14x+24bethegivenpolynomail.Thefactorsofthecons\tan t \\ term24inthispolynomailare\pm 1,\pm 2,\pm 3,\pm 4,\pm 6,\pm 8,\pm 12and\pm 24. \\ Wehave, \\ f\left(2\right)=2^3-2^2-14\left(2\right)+24=0 \\ \Rightarrow \left(x-2\right)isafactoroff\left(x\right). \\ similarly,itcanbeverifiedthat(x-3)and(x+4)arefactorsoff\left(x\right). \\ Sincef\left(x\right)isapolynomailofdegree3.Soitcannothavemorethan3linearfactors. \\ Hence,f\left(x\right)=k(x-2)(x-3)(x+4),wherekisacon\tan t \end{gathered}$$
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