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Callisto
 3 years ago
Polynomials #1
Question 41
It is given that f(3x) = 54x^3 27x^2 +px +q. When f(x) is divided by (x3), the remainder is 42.
Find the remainder when f(x/3) is divided by x9
*Note: I'm helping my sister but I'm in trouble too :*
Callisto
 3 years ago
Polynomials #1 Question 41 It is given that f(3x) = 54x^3 27x^2 +px +q. When f(x) is divided by (x3), the remainder is 42. Find the remainder when f(x/3) is divided by x9 *Note: I'm helping my sister but I'm in trouble too :*

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FoolForMath
 3 years ago
Best ResponseYou've already chosen the best response.0I thought someone was typing an answer.

cwtan
 3 years ago
Best ResponseYou've already chosen the best response.0TT bluring....... btw i found 4.... I duno whether it is right or wrong...

Callisto
 3 years ago
Best ResponseYou've already chosen the best response.0The answer is not 4 :

cwtan
 3 years ago
Best ResponseYou've already chosen the best response.0younger sister? it's complicated... LOL

Ishaan94
 3 years ago
Best ResponseYou've already chosen the best response.3Lol this question is funny.

Callisto
 3 years ago
Best ResponseYou've already chosen the best response.0How did you get that answer? @Ackhat

ash2326
 3 years ago
Best ResponseYou've already chosen the best response.0We have \[f(3x)=54x^327x^2+px+q\] It can be written as \[f(3x)=2(3x)^33(3x)^2+\frac p 3 (3x) +q\] so \[f(x)=2x^33x^2+\frac p 3 x+q\] We are given that when f(x) is divided by (x3) the remainder is 42 so Using remainder theorem \[f(3)=42\] Now you can find P+q from here, Next find \(f(\frac x 3)\) to find the remainder when f(x/3) is divided by (x9) put x=9 in f(x/3)

Callisto
 3 years ago
Best ResponseYou've already chosen the best response.0.... I've thought about it.....I swear......

Ishaan94
 3 years ago
Best ResponseYou've already chosen the best response.3f(x)/(x3)=k+42/(x3) 3f(x/3)/(x9)= k + 3*42/(x9)

Ackhat
 3 years ago
Best ResponseYou've already chosen the best response.1i simpy divide by x3 and got p+q=15 and after by x9 and got that the reminder is p+q+27

Callisto
 3 years ago
Best ResponseYou've already chosen the best response.0Hold on... @Ishaan94 How does it work: 3f(x/3)/(x9)= k + 3*42/(x9)? @Ackhat Do you mean you divided the equation f(x) by (x3) first, then divide f(x) by (x9)? or ...?

Ishaan94
 3 years ago
Best ResponseYou've already chosen the best response.3\[\frac{f(x)}{x3} = P(x) + \frac{42}{x3}\]\[x = \frac{x}{3}\] \[\frac{3\cdot f\left(x/3\right)}{x9} = P(x) + \frac{42\cdot 3}{x9}\] I love my solution <3

Callisto
 3 years ago
Best ResponseYou've already chosen the best response.0Okay, got it. My calculation mistake : @Ackhat

Callisto
 3 years ago
Best ResponseYou've already chosen the best response.0@Ishaan94 More explanation is appreciated :) (sorry... I'm stupid : )

FoolForMath
 3 years ago
Best ResponseYou've already chosen the best response.0Beautiful solution Ishaan.

FoolForMath
 3 years ago
Best ResponseYou've already chosen the best response.0Calli: Division Algorithm

Ishaan94
 3 years ago
Best ResponseYou've already chosen the best response.3I am not a good teacher, Sorry. What part you didn't understand callisto?

Ishaan94
 3 years ago
Best ResponseYou've already chosen the best response.3Thank you very much foolformath

Callisto
 3 years ago
Best ResponseYou've already chosen the best response.0\[\frac{3\cdot f\left(x/3\right)}{x9} = P(x) + \frac{42\cdot 3}{x9}\] ^ don't know where it comes..

cwtan
 3 years ago
Best ResponseYou've already chosen the best response.0What a simple solution!!! Great job @Ishaan94 !!!!!

FoolForMath
 3 years ago
Best ResponseYou've already chosen the best response.0Substitute \(x=\frac x3 \) in \[ \frac{f(x)}{x3} = P(x) + \frac{42}{x3} \]

Callisto
 3 years ago
Best ResponseYou've already chosen the best response.0Oh... Got it!!!! Thanks!!! Lovely solution :)

Ishaan94
 3 years ago
Best ResponseYou've already chosen the best response.3Okay. \[\large\frac{f\left(\frac{x}{3}\right)}{\frac{x}33} = P + \frac{42}{\frac x33}\]Where P is any quadratic polynomial. \[\large \implies \frac{f\left(\frac x3\right)}{\frac{x9}3} = P + \frac{42}{\frac {x 9}3}\]

FoolForMath
 3 years ago
Best ResponseYou've already chosen the best response.0No, it is beautiful :

Ishaan94
 3 years ago
Best ResponseYou've already chosen the best response.3What's 'Bezu'? @Akchat

Callisto
 3 years ago
Best ResponseYou've already chosen the best response.0The most wonderful thing is that my sister understands it :) Once again, thank you everyone :)
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