We know:
Subtracting the latter from the former, we find:
Let and we may write:
Hence the remainder is .
When a polynomial f(x) is divided by x-1 and x-2, the remainders are 0 and -4 respectively. Find the remainder
when f(x) is divided by (x-1)(x-2).
The answer of this question is -4x+4
Can anyone show me how to work out the solution of this question? Thanks
You don't have to let Q3 = Q2-Q1, it's just to make it easier to se that when we subtract the later from the former we actually get a new quotient with a new remainder which we want to write so that we have f(x)/((x-1)(x-2)) and r/((x-1)(x-2)). And in this case r = 4(1-x)
Thank you very much. I understand this question now.
However, I still can't solve the following two questions
1. f(x) is a polynomial. When 3x-2 divides f(x) , the remainder is K. when 2-3x divides f(x) , the remainder is
the answer is K.
I try to set up this way following your method to last question,
3x-2/f(x) = Q1(x) + K/f(x)
so 2-3x/f(x) = -(3x-2) / f(x) + Q1(x) + (-k)/f(x)
so the answer show be -K which is different from the textbook answer.
2) Let f(x) be a polynomial. If f(x) is divisible by x-1, which of the following must be a factor of f(2x+1)?
the answer is x
I have no idea how to do this question at all.
Please help me . Thank you.