Help with polinomials:
If
p(x) = x^4 - ax^3 + (a-b)x^2 + (b^2)x +a +2
q(x) = x^2 - ax -b

The remainder of the division between p(x) and q(x) is equal to c. Find a+b+c

I am trying to use the remainder theorem, but i need to factorize those two things, and that seems impossible.
Ani idea , tanks.

Question

Help with polinomials:
If
p(x) = x^4 - ax^3 + (a-b)x^2 + (b^2)x +a +2 
q(x) = x^2 - ax -b

The remainder of the division between p(x) and q(x) is equal to c. Find a+b+c
 
I am trying to use the remainder theorem, but i need to factorize those two things, and that seems impossible.
Ani idea , tanks.

anonymous · Answer

attachment

anonymous · Answer

Do you know how to do long division?

anonymous · Answer

according to remainder theorem u can write$$p(x)=q(x) \ (x^2+dx+e)+c$$just substitute $p(x)$ and $q(x)$ and then equate the coefficients of both sides to finding $a,b,c,d,e$

anonymous · Answer

thats not a good ide for a test :) so lets think to find another one :)

anonymous · Answer

have u tried long division?

anonymous · Answer

Well, i´ve tried long division and i find that the remainder is equal to 
a^2 + b^2 + a + ab + 2

So i´m supposed to make that equals to c and find a+b+c, but it´s impossible since i have three unknowns.

Even making trial and error with the alternatives, i can´t get it.

anonymous · Answer

yes its weird !!! remainder is $(a^2+b^2)x+a+ab+2$ so$$a^2+b^2=0$$$$a+ab+2=c$$but still nothing

anonymous · Answer

I think i got it!!

Well, a^2+b^2 = 0, only if both a and b equals 0, so we left, c=2

And then a+b+c = 2

Is that right?

anonymous · Answer

ahh, yes :) those are real numbers :) You made it :)

anonymous · Answer

Nice!, thank you.

anonymous · Answer

yw :)