Hi:
I have come across a question but have not been able to work out a method to solve this, yet
When x^3+3x^2+ax+2 is divided by x – 2 the remainder is 4. Find a.
Any help. thanks
err - most help. thanks
most definitely high school ...
Synthetic Division
Basic theorem: if P(x) is a polynomial and dividing by x-b gives quotient Q(x) with remainder R (which is a constant, a number) then P(x)/(x-b)= Q(x)+ R/(x-b) so P(x)= Q(x)(x- b)+ R. Setting x= b, P(b)= Q(b)(b-b)+ R= R no matter what Q(b) is. That is, the remainder when P(x) is divided by x- b is the value of P(b).
Here, P(2)= 2^4+ 3(2^2)+ a(2)+ 2= 16+ 3(4)+ 2a+ 2= 2a+ 30. What value of a makes that equal to 4?
So, is this right?
x^3+bx^2-15x+3 divided by x+1 remainder 14: Find b
1: 1 b -15 3
1 1+b -14+b
1 1+b -14+b 17+b
17+b=14
b=-3
If this is so, it mean that in the case of the last column, where -14 is under the 3, I ignore the minus sign and just make addition with integer.
But in the case of the 3rd column, I can't ignore the minus sign on the 15, cause it is the starting number?
thanks
So, is this right?
x^3+bx^2-15x+3 divided by x+1 remainder 14: Find b
1:::::1 b -15 3
1 1+b -14+b
1 1+b -14+b 17+b
17+b=14
b=-3
If this is so, it mean that in the case of the last column, where -14 is under the 3, I ignore the minus sign and just make addition with integer.
But in the case of the 3rd column, I can't ignore the minus sign on the 15, cause it is the starting number?
thanks