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Question Number 33789 by wath trine last updated on 24/Apr/18

$$\mathrm{If}\mathrm{the}\mathrm{equation}2x^2+14x-15=0\mathrm{is}$$$$\mathrm{divided}\mathrm{by}(x-4),\mathrm{the}\mathrm{remainder}\mathrm{is}$$

Answered by MJS last updated on 25/Apr/18

$$(2x^2+14x-15)/(x-4)=2x$$$$2x(x-4)=2x^2-8x$$$$2x^2+14x-15-(2x^2-8x)=22x-15$$$$(22x-15)/(x-4)=22$$$$22(x-4)=22x-88$$$$22x-15-(22x-88)=73=\mathrm{remainder}$$$$$$$$\frac{2x^2+24x-15}{x-4}=2x+22+\frac{73}{x-4}$$

Commented by Rasheed.Sindhi last updated on 25/Apr/18

$${\mathrm{Didn}}^{\prime }\mathrm{t}\mathrm{understand}\mathrm{first}\mathrm{statement}:$$$$(2x^2+14x-15)/(x-4)=2x$$$$$$

Commented by MJS last updated on 25/Apr/18

$${\mathrm{it}}^{\prime }\mathrm{s}\mathrm{a}\mathrm{polynome}\mathrm{division}\mathrm{in}\mathrm{steps}$$$$1.\mathrm{step}:x\times ?=2x^2\Rightarrow 2x$$$$2.\mathrm{step}:2x(x-4)=2x^2-8x$$$$3.\mathrm{step}:2x^2+14x-15-(2x^2-8x)=22x-15$$$$1.\mathrm{step}:x\times ?=22x...$$$$...$$

Commented by Rasheed.Sindhi last updated on 25/Apr/18

$$\mathbb{T}\mathrm{h}\alpha \mathrm{n}\mathbb{k}\mathcal{SS}ir!$$

Commented by Joel578 last updated on 25/Apr/18

$$\mathrm{It}\mathrm{is}\mathrm{long}\mathrm{polynomial}\mathrm{division}$$

Commented by Rasheed.Sindhi last updated on 25/Apr/18

$$\mathrm{Yes}\mathrm{sir}\mathrm{I}\mathrm{understood}.$$

Answered by tawa tawa last updated on 24/Apr/18

$$\mathrm{f}\left(\mathrm{x}\right)={2\mathrm{x}}^2+14\mathrm{x}-15$$$$\mathrm{But}:\mathrm{x}-4=0,\Rightarrow \mathrm{x}=4$$$$\therefore \mathrm{f}\left(4\right)=2{\left(4\right)}^2+14\left(4\right)-15$$$$\therefore \mathrm{f}\left(4\right)=2\left(16\right)+56-15$$$$\therefore \mathrm{f}\left(4\right)=32+56-15$$$$\therefore \mathrm{f}\left(4\right)=73$$$$\mathrm{Therefore},\mathrm{the}\mathrm{remainder}\mathrm{is}73$$

Answered by $@ty@m last updated on 25/Apr/18

Commented by MJS last updated on 26/Apr/18

$$\mathrm{thank}\mathrm{you},\mathrm{I}{\mathrm{didn}}^{\prime }\mathrm{t}\mathrm{remember}\mathrm{this}...$$

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