Question

lim x->∞ (2x²+3x+1/3x³+x+2)=_​

Answer 1

Answer:

The trick to this is basically, every time you subtract from part of polynomial, find a way to eliminate the term with the highest power of x. For example,in (1) we have x^4+3x^3. Here, we want to remove x^4. To do so, we need to find a term, such that when multiplied with (x+2), we can get an x^4. So we see that the term would be x^3, as x^3(x+2) gives us x^4+2x^3.

So, we subtract that away from the polynomial, and we get x^3 as a remainder. Repeat this process until the remainder’s x power is one less than the divisor’s power of x (In this case, remainder is -8, which has the term x^0, one less than x^1 in the divisor (x+2)

To obtain final answer, take the numbers you have placed on top, then add the remainder divided by the divisor to get the final answer.

To check, use remainder theorem and sub x=-2 and you will obtain -8.

Step-by-step explanation: