SOLUTION: Find the value of the constants A, B, C and D in the following identity: {{{ x^3-6x^2+11x+x=(x-2)(Ax^2+Bx+C)+ D }}}.

Algebra ->  Functions -> SOLUTION: Find the value of the constants A, B, C and D in the following identity: {{{ x^3-6x^2+11x+x=(x-2)(Ax^2+Bx+C)+ D }}}.      Log On


   

Question 387819: Find the value of the constants A, B, C and D in the following identity:
+x%5E3-6x%5E2%2B11x%2Bx=%28x-2%29%28Ax%5E2%2BBx%2BC%29%2B+D+.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!

+x%5E3-6x%5E2%2B11x%2Bx+=%28Ax%5E3%2BBx%5E2%2BCx%29%2B%28-2Ax%5E2-2Bx-2C%29%2BD
+x%5E3-6x%5E2%2B11x%2Bx+=Ax%5E3%2B%28B-2A%29x%5E2%2B%28C-2B%29x%2B%28D-2C%29+
Compare terms,
highlight%28+A=1%29
Then,
B-2=-6
highlight%28B=-4%29
Then,
C-2%28-4%29=11
C%2B8=11
highlight%28C=3%29
Then,
D-6=1
highlight%28D=7%29