anonymous
  • anonymous
how can i create a polynomial my own third degree polynomial that when divided by x + 2 has a remainder of –4?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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JamesJ
  • JamesJ
Suppose 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
  • anonymous
what would the equation look like when written out?
JamesJ
  • JamesJ
Well, 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?

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anonymous
  • anonymous
i have no idea
JamesJ
  • JamesJ
What is an example of a second order polynomial?
JamesJ
  • JamesJ
What's the definition of a nth order polynomial?
JamesJ
  • JamesJ
A 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
  • anonymous
-x^3-3x^2-2x this is what i got !
anonymous
  • anonymous
|dw:1328602800912:dw|
JamesJ
  • JamesJ
That polynomial when divided by x+2 has zero remainder.
anonymous
  • anonymous
i give up .. but the idea the same ..
JamesJ
  • JamesJ
@waleed: Again, you're going down the wrong track. \[ -x^3-3x^2-2x = -x (x^2 + 3x + 2) = -x(x+1)(x+2) \] Hence \( -x^3-3x^2-2x \) 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
  • anonymous
okey so we have to say p(x)= {(x+2)(x^2+x+1)} - 4 ????
JamesJ
  • JamesJ
That's one solution, yes.
JamesJ
  • JamesJ
Here's another. Choose \( Q(x) = x^2 \) and hence \[ P(x) = (x+2)x^2 -4 \] \[= x^3 + 2x^2 - 4 \]
anonymous
  • anonymous
okey ..Bow my hat ! Thnx for information i will delete my post .. so it will no show wrong solution

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