ok, the answer is x^2 - 2x +6. You are being asked what is
(x^3 +x^2 +18) / (x+3)
Solve this by comparing co-efficients .....as below
Let x^3 +x^2 +18 = (x+3)(ax^2 +bx +c)
then a=1,by comparing the co-efficients of x^3
now by comparing co-efficients of x^2, 3a +b =1 so b= -2
and comparing constants, 3c =18 so c=6
which gives
x^3 +x^2 +18 =(x+3)(x^2 -2x +6)
You could write it as { (x^2-2x+6) }^ (-1), then use the Binomial Theorem to give you an infinite power series,but that's about it. That would also be very messy and long-winded.
Is there a particular problem that you are trying to solve?
x3 + x2 + 18
x + 3
It's a multiple choice question and none of the choices are fractions...
A. x2 + 2x + -6
B. x2 + -4x + 15
C. x + 6
D. x2 + 15
E. x2 + -2x + 6
ok, the answer is x^2 - 2x +6. You are being asked what is
(x^3 +x^2 +18) / (x+3)
Solve this by comparing co-efficients .....as below
Let x^3 +x^2 +18 = (x+3)(ax^2 +bx +c)
then a=1,by comparing the co-efficients of x^3
now by comparing co-efficients of x^2, 3a +b =1 so b= -2
and comparing constants, 3c =18 so c=6
which gives
x^3 +x^2 +18 =(x+3)(x^2 -2x +6)
