SOLUTION: The remainder when x+3 divides x^4+7x^3-15x^2-8x+m is 23. find the value of m. could you explain step by step the procedure? thanks

Question 151345: The remainder when x+3 divides x^4+7x^3-15x^2-8x+m is 23. find the value of m.
could you explain step by step the procedure?
thanks
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The remainder when x+3 divides x^4+7x^3-15x^2-8x+m is 23. find the value of m.
:
Use synthetic division:
:
.....____________________
-3|1 + 7 - 15 - 8 + m
..........-3 - 12 + 81 - 219
.....------------------------
.......1 + 4 - 27 + 73 + 23
:
Note we included the remainder, and m
We ask,"What value of m, if 219 is subtracted, give us 23:
An equation for this statement would be:
:
-219 + m = 23
m = 23 + 219
m = 242
:
you can check this using normal long division
;
...........---------------------------------
(x+3)|x^4 + 7x^3 - 15x^2 + 8x + 242
;
See if you can do this. Let me know if you have difficulty with this.
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