\(If\quad f\left( x+3 \right) \quad =\quad { x }^{ 2 }+x-6,\quad then\quad find\quad f(x).\quad\)

\(If\quad f(x+3)\quad =\quad { x }^{ 2 }-7x+2,\quad find\quad the\quad remainder\quad when\quad f(x)\quad is\quad divided\quad by\quad x+1.\)

Please help me with the problems, **Thanks!**

## Comments

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TopNewestThey are very easy.

1.\(\text{Let g(x) = f(x), Not let y = x+3, we get} \\ g(y) = (y-3)^2 + (y-3) - 6 \\ f(x) = x^2 - 5x\)

2.\(\text{We know that the remainder will be f(-1). We have to find f(-1) } \\ \text{We know that } f(x+3) = x^2 -7x +2 \\ \text{Now if we let x = -4 we'll get f(-1) hence our answer.} \\ \text{Hence f(-1) will be} f(-1) = (-4)^2 - 7(4) + 2 = 46 \) – Rajdeep Dhingra · 1 year, 11 months ago

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@Swapnil Das @Sravanth Chebrolu I think you must revise the simple remainder- theorem for the 2nd question. – Nihar Mahajan · 1 year, 11 months ago

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@Nihar Mahajan – Swapnil Das · 1 year, 11 months ago

Yup, I have. I just got a last doubt in the chapter, so I asked for help. Well I was now solving problems of Newton's Sums.Log in to reply

let, x+3 =y......

make a new function.....

and solve.... – Parth Tandon · 1 year, 11 months ago

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– Parth Tandon · 1 year, 11 months ago

i think i am little slow in typing.......:pLog in to reply

– Sravanth Chebrolu · 1 year, 11 months ago

Why do you think so?Log in to reply

– Parth Tandon · 1 year, 11 months ago

when i started posting the solution there were no comments but as soon as i finished i found 6 comments hovering around....:)Log in to reply

– Sravanth Chebrolu · 1 year, 11 months ago

Whoah! That happens to me too! But, don't consider that as your inability.Log in to reply

i am working on it......

always used to work with a pen and paper so.................. – Parth Tandon · 1 year, 11 months ago

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– Sravanth Chebrolu · 1 year, 11 months ago

Oh yes! The classic method of pen and paper . . . :PLog in to reply

can someone tell me what is multi_step decryption.....? – Parth Tandon · 1 year, 11 months ago

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First question:the answer is \(x^{2}-5x\)Second question:the answer is \(46\).Am I right? If I am I'll post the solution. Please reply @Swapnil Das – Sravanth Chebrolu · 1 year, 11 months ago

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– Rajdeep Dhingra · 1 year, 11 months ago

Ur answer to 2nd one is wrong. For a level 5 like U it should Child's play. Anyways u can see my solution. Cheers!Log in to reply

– Sravanth Chebrolu · 1 year, 11 months ago

Sorry, I got it wrong as I got meddled up with the signs, I posted it correctly on Swapnil's message board though, cheers! xDLog in to reply

– Swapnil Das · 1 year, 11 months ago

Yeah!Log in to reply

link! – Sravanth Chebrolu · 1 year, 11 months ago

Hey! I posted a question on logic just now, as you wanted me to post such questions I did it, here's theLog in to reply

– Swapnil Das · 1 year, 11 months ago

See who have solved...Log in to reply

– Sravanth Chebrolu · 1 year, 11 months ago

Omg! That was qiuck! Hope you liked it. . .Log in to reply

– Swapnil Das · 1 year, 11 months ago

Hey Sravanth, I don't know how I am getting some other remainder. Can you post the 2nd solution please?Log in to reply

As you know how to make expression, you'll get \(f(x):x^2-13x-10\)

Dividing it by \(x+1\), we get \(4\). . . – Sravanth Chebrolu · 1 year, 11 months ago

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– Swapnil Das · 1 year, 11 months ago

Can you please tell me how it became -5y instead of -5x?Log in to reply

– Sravanth Chebrolu · 1 year, 11 months ago

BTW, I liked the new look of Brilliant! But I didn't find the explore icon anywhere. . .Log in to reply

– Parth Tandon · 1 year, 11 months ago

community.............Log in to reply

explore, I didn't find that... – Sravanth Chebrolu · 1 year, 11 months agoLog in to reply

i think explore renamed to community................

latest posts are there which before were given under explore................ – Parth Tandon · 1 year, 11 months ago

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– Sravanth Chebrolu · 1 year, 11 months ago

Yes. I saw that. Thank you very much!Log in to reply

do u know what is multi step decryption or i hv to search on net.....? – Parth Tandon · 1 year, 11 months ago

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Digital Fortress, but I don't know much about it. . . :( – Sravanth Chebrolu · 1 year, 11 months agoLog in to reply

thnx for giving a thought to it.................. – Parth Tandon · 1 year, 11 months ago

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– Sravanth Chebrolu · 1 year, 11 months ago

Welcome!Log in to reply

– Parth Tandon · 1 year, 11 months ago

multi step decryption...............?Log in to reply

– Swapnil Das · 1 year, 11 months ago

May I help U?Log in to reply

multi step decryption....? – Parth Tandon · 1 year, 11 months ago

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– Sravanth Chebrolu · 1 year, 11 months ago

Sorry, that was a typo there! It's edited now.Log in to reply

– Swapnil Das · 1 year, 11 months ago

I think you are right. Please post the solution.Log in to reply

– Sravanth Chebrolu · 1 year, 11 months ago

But I think it's already posted! :PLog in to reply

– Swapnil Das · 1 year, 11 months ago

Well Rajdeep also did the same, BTW thank you very much. Just a request, if you have time anytime, please post problems of this format, I would surely like them!Log in to reply

Surely! I'll keep posting suchquestions! – Sravanth Chebrolu · 1 year, 11 months ago

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– Swapnil Das · 1 year, 11 months ago

Go to Community-All topics-ProblemsLog in to reply

explore? – Sravanth Chebrolu · 1 year, 11 months agoLog in to reply

– Swapnil Das · 1 year, 11 months ago

yeah!Log in to reply

– Sravanth Chebrolu · 1 year, 11 months ago

Thank you very much! BTW, how did you like the new look?Log in to reply

– Swapnil Das · 1 year, 11 months ago

Nice!Log in to reply