A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 4 years ago
how can i create a polynomial my own third degree polynomial that when divided by x + 2 has a remainder of –4?
anonymous
 4 years ago
how can i create a polynomial my own third degree polynomial that when divided by x + 2 has a remainder of –4?

This Question is Closed

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.1Suppose P(x) is your polynomial. If when divided by (x+2) it has a remainder of 4, then that means we can write P(x) = (x+2)Q(x)  4 for some other polynomial Q(x). Hence to answer your question, choose any polynomial Q(x) such that P(x) is third order. That is, make Q(x) an arbitrary second order polynomial.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0what would the equation look like when written out?

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.1Well, after you've chosen a Q(x), you can expand it and see. What's the simplest second order polynomial Q(x) you can think of?

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.1What is an example of a second order polynomial?

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.1What's the definition of a nth order polynomial?

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.1A polynomial is a finite sum of monomials, such as x, 2x, 5x, x^3, 17x^4, etc. The order of a polynomial is the highest power of x in the monomials. For example x, 2x, 17x, 5x + 3 are all examples of first order polynomials. x^2, 3x^2, x^2 + x, x^2 + 5, x^2  18x + 25959 are all examples of second order polynomials x^3 is a third order polynomial, as is (x+1)^3 = x^3 + 3x^2 + 3x + 1 Make sense?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0x^33x^22x this is what i got !

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1328602800912:dw

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.1That polynomial when divided by x+2 has zero remainder.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i give up .. but the idea the same ..

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.1@waleed: Again, you're going down the wrong track. \[ x^33x^22x = x (x^2 + 3x + 2) = x(x+1)(x+2) \] Hence \( x^33x^22x \) divided by \( x+2 \) has zero remainder. ======= The way to solve the problem is as I've laid out above. Find a polynomial Q(x) of second order and hence define a polynomial P(x) where \[ P(x) = (x+2)Q(x)  4 \]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0okey so we have to say p(x)= {(x+2)(x^2+x+1)}  4 ????

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.1That's one solution, yes.

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.1Here's another. Choose \( Q(x) = x^2 \) and hence \[ P(x) = (x+2)x^2 4 \] \[= x^3 + 2x^2  4 \]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0okey ..Bow my hat ! Thnx for information i will delete my post .. so it will no show wrong solution
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.