A community for students.
Here's the question you clicked on:
 0 viewing
Callisto
 2 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
 2 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 :*

This Question is Closed

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

cwtan
 2 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
 2 years ago
Best ResponseYou've already chosen the best response.0The answer is not 4 :

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

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

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

ash2326
 2 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
 2 years ago
Best ResponseYou've already chosen the best response.0.... I've thought about it.....I swear......

Ishaan94
 2 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
 2 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
 2 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
 2 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
 2 years ago
Best ResponseYou've already chosen the best response.0Okay, got it. My calculation mistake : @Ackhat

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

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

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

Ishaan94
 2 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
 2 years ago
Best ResponseYou've already chosen the best response.3Thank you very much foolformath

Callisto
 2 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
 2 years ago
Best ResponseYou've already chosen the best response.0What a simple solution!!! Great job @Ishaan94 !!!!!

FoolForMath
 2 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
 2 years ago
Best ResponseYou've already chosen the best response.0Oh... Got it!!!! Thanks!!! Lovely solution :)

Ishaan94
 2 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
 2 years ago
Best ResponseYou've already chosen the best response.0No, it is beautiful :

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

Callisto
 2 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 :)
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.