I'm having problems with two questions from my hw. I have no idea where to even start to solve the problems. Please help as much as you can!! Thanks!
1. When x^3 - 7x + 4 is divided by the polynomial D(x), the quotient is x^2 - 3x + 2 and the remainder is -2. Find D(x).
2. Find k so that when x^3 + kx^2 + k^2x + 14 is divided by x+2, the remainder is 0.
Alright , lets come back to this equation .
DO some regrouping .
So now we compare ..
x^3=x^3 ( there is nothing to compare)
0x^2=-(a+3)x^2 , cancel the x^2 and solve for a .
-7x=(3a+2)x , cancel the x and solve for a
the last one , the constant , do the same comparing .
All of these comparisons give a so you will only have to compare one of them .
Hope this helps. Any more doubts ?
Alright , lets come back to this equation .
DO some regrouping .
So now we compare ..
( there is nothing to compare)
, cancel the and solve for a .
, cancel the x and solve for a
the last one , the constant , do the same comparing .
All of these comparisons give a so you will only have to compare one of them .
Hope this helps. Any more doubts ?