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- anonymous

how can i create a polynomial my own third degree polynomial that when divided by x + 2 has a remainder of –4?

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- anonymous

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- 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

what would the equation look like when written out?

- 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

i have no idea

- JamesJ

What is an example of a second order polynomial?

- JamesJ

What's the definition of a nth order polynomial?

- 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

-x^3-3x^2-2x
this is what i got !

- anonymous

|dw:1328602800912:dw|

- JamesJ

That polynomial when divided by x+2 has zero remainder.

- anonymous

i give up .. but the idea the same ..

- 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

okey so we have to say
p(x)= {(x+2)(x^2+x+1)} - 4
????

- JamesJ

That's one solution, yes.

- JamesJ

Here's another. Choose \( Q(x) = x^2 \) and hence
\[ P(x) = (x+2)x^2 -4 \] \[= x^3 + 2x^2 - 4 \]

- anonymous

okey ..Bow my hat !
Thnx for information i will delete my post .. so it will no show wrong solution

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