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Question Number 79866 by 09264910412 last updated on 28/Jan/20

$$Chapter\left(2\right)$$$$RemainderTheorem$$$$and$$$$FactorTheorem$$$$Exercises(2.1)$$$$\mathbf{Remainder}\mathrm{T}\mathbf{hrorem}$$$$1.\mathrm{Find}\mathrm{the}\mathrm{remainder}\mathrm{when}{\mathbf{x}}^8+2\mathbf{x}-5$$$$\mathrm{is}\mathrm{divided}\mathrm{by}(\mathrm{x}-1).$$$$2.\mathrm{Find}\mathrm{the}\mathrm{remainder}\mathrm{when}{2\mathrm{x}}^{2}13\mathrm{x}+10$$$$\mathrm{is}\mathrm{divided}\mathrm{by}(\mathrm{x}-3).$$

Commented by TawaTawa last updated on 28/Jan/20

$$\left(1\right)$$$$\mathrm{let}\mathrm{x}-1=0$$$$\therefore \mathrm{x}=1$$$$\mathrm{Hence},\mathrm{remainder}={\left(1\right)}^8+2\left(1\right)-5$$$$\therefore \mathrm{remainder}=1+2-5$$$$\therefore \mathrm{remainder}=-2$$$$$$$$\left(2\right)$$$$\mathrm{let}\mathrm{x}-3=0$$$$\therefore \mathrm{x}=3$$$$\mathrm{Hence},\mathrm{remainder}=2{\left(3\right)}^2+13\left(3\right)+10(\mathrm{i}\mathrm{assume}+13\mathrm{x})$$$$\therefore \mathrm{remainder}=2\left(9\right)+39+10$$$$\therefore \mathrm{remainder}=18+39+10$$$$\therefore \mathrm{remainder}=67$$$$$$

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