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

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

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

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## 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.$\text{We know that the remainder will be f(-1). We have to find f(-1) } \\ \text{We know that } f(x+3) = x^2 -7x +2 \\ \text{Now if we let x = -4 we'll get f(-1) hence our answer.} \\ \text{Hence f(-1) will be} f(-1) = (-4)^2 - 7(4) + 2 = 46$

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@Swapnil Das @Sravanth Chebrolu I think you must revise the simple remainder- theorem for the 2nd question.

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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. @Nihar Mahajan

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

make a new function.....

and solve....

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i think i am little slow in typing.......:p

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Why do you think so?

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i am working on it......

always used to work with a pen and paper so..................

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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

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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!

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

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link!

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

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I think you are right. Please post the solution.

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But I think it's already posted! :P

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Surely! I'll keep posting suchquestions!

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explore?Log in to reply

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Can you please tell me how it became -5y instead of -5x?

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Sorry, that was a typo there! It's edited now.

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

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multi step decryption....?

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explore, I didn't find that...Log in to reply

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

latest posts are there which before were given under explore................

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do u know what is multi step decryption or i hv to search on net.....?

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Digital Fortress, but I don't know much about it. . . :(Log in to reply

thnx for giving a thought to it..................

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

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Sure. Here it is.

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

Dividing it by $x+1$, we get $4$. . .

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can someone tell me what is multi_step decryption.....?

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