Polynomial p(x) and a divisor d(x) are given. Find the quotient q(x) and the remainder r(x) when p(x) is divided by d(x).
a,
p(x)=12x^3-40x^2+11x+39
d(x)=2x-5
b,
p(x)=x^4+x^2+2
d(x)=x^2+x+1
This is just long division of polynomials. I'll walk you through the first one.
We need to find the correct multiple of to get to the level of . That multiple is .
So we multiply and subtract that from , which leaves us with . Now, how many times will go into this? .
So and we subtract out , leaving us with . Finally, we see that we need a multiple of -7 for the last step:
and we subtract this from to yield 4.
The answer is therefore:
Hello,
Here is a method, it's the one I apply, it's not necessarily the one you have to use.
I see what the highest degree in p(x) is, and I find how to multiply x powered to the highest degree to get the first term of p(x).
So I'll write :
Then I'll do it again, with -10x² :
--->
And continue, again and again...