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 4x - 12

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 (x - 1)

k(x + 1)(x - 1)

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

k(x + 1)(x - 1)(x - 3)

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 (x - a) but, instead, of the form (x^2 - a), 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 4x - 12