Urgent! Help! A cubic polynomial has zeros at x=-1, x=1, and x=3. It has a y-intercept of -6. What is the remainder when we divide this polynomial by x^2+1 ??

1 Answer
Oct 29, 2016

I used WolframAlpha to do the division the remainder is 4x12

Explanation:

Start is a factor, k that allows one to adjust the y intercept:

k

Multiply that by the factor corresponding to the zero, x=1 -- that is (x+1)

k(x+1)

Multiply by the factor corresponding to the zero, x=1 -- that is (x1)

k(x+1)(x1)

The last factor is the one corresponding to the zero, x=3 -- (x3)

k(x+1)(x1)(x3)

To find the value of k, we set the factors equal to -6 and x within the factors equal to 0

6=k(+1)(1)(3)

k=2

Because the divisor is not of the form (xa) but, instead, of the form (x2a), one cannot use the remainder theorem. Therefore, the only way to find the remainder is by using division.

Here is a link to WolframAlpha for the division.

Please notice that the remainder is 4x12