Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
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 :*
 one year ago
 one year 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 :*
 one year ago
 one year ago

This Question is Closed

FoolForMathBest ResponseYou've already chosen the best response.0
I thought someone was typing an answer.
 one year ago

cwtanBest ResponseYou've already chosen the best response.0
TT bluring....... btw i found 4.... I duno whether it is right or wrong...
 one year ago

CallistoBest ResponseYou've already chosen the best response.0
The answer is not 4 :
 one year ago

cwtanBest ResponseYou've already chosen the best response.0
younger sister? it's complicated... LOL
 one year ago

Ishaan94Best ResponseYou've already chosen the best response.3
Lol this question is funny.
 one year ago

CallistoBest ResponseYou've already chosen the best response.0
How did you get that answer? @Ackhat
 one year ago

ash2326Best ResponseYou've already chosen the best response.0
We 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)
 one year ago

CallistoBest ResponseYou've already chosen the best response.0
.... I've thought about it.....I swear......
 one year ago

Ishaan94Best ResponseYou've already chosen the best response.3
f(x)/(x3)=k+42/(x3) 3f(x/3)/(x9)= k + 3*42/(x9)
 one year ago

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

CallistoBest ResponseYou've already chosen the best response.0
Hold 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 ...?
 one year ago

AckhatBest ResponseYou've already chosen the best response.1
f(x)/(x3) f(x/3)/(x9)
 one year ago

Ishaan94Best 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
 one year ago

CallistoBest ResponseYou've already chosen the best response.0
Okay, got it. My calculation mistake : @Ackhat
 one year ago

CallistoBest ResponseYou've already chosen the best response.0
@Ishaan94 More explanation is appreciated :) (sorry... I'm stupid : )
 one year ago

FoolForMathBest ResponseYou've already chosen the best response.0
Beautiful solution Ishaan.
 one year ago

FoolForMathBest ResponseYou've already chosen the best response.0
Calli: Division Algorithm
 one year ago

Ishaan94Best ResponseYou've already chosen the best response.3
I am not a good teacher, Sorry. What part you didn't understand callisto?
 one year ago

Ishaan94Best ResponseYou've already chosen the best response.3
Thank you very much foolformath
 one year ago

CallistoBest 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..
 one year ago

cwtanBest ResponseYou've already chosen the best response.0
What a simple solution!!! Great job @Ishaan94 !!!!!
 one year ago

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

CallistoBest ResponseYou've already chosen the best response.0
Oh... Got it!!!! Thanks!!! Lovely solution :)
 one year ago

Ishaan94Best ResponseYou've already chosen the best response.3
Okay. \[\large\frac{f\left(\frac{x}{3}\right)}{\frac{x}33} = P + \frac{42}{\frac x33}\]Where P is any quadratic polynomial. \[\large \implies \frac{f\left(\frac x3\right)}{\frac{x9}3} = P + \frac{42}{\frac {x 9}3}\]
 one year ago

FoolForMathBest ResponseYou've already chosen the best response.0
No, it is beautiful :
 one year ago

Ishaan94Best ResponseYou've already chosen the best response.3
What's 'Bezu'? @Akchat
 one year ago

CallistoBest ResponseYou've already chosen the best response.0
The most wonderful thing is that my sister understands it :) Once again, thank you everyone :)
 one year ago
See more questions >>>
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.