How do you use the remainder theorem and Synthetic Division to find the remainders in the following division problems −2x4−6x2+3x+1 divided by x+1?

1 Answer
George C.
Jul 30, 2015

Let f(x)=−2x4−6x2+3x+1.

Using the remainder theorem, the remainder is

f(−1)=−2−6−3+1=−10

Using Synthetic division we get the same remainder.

Explanation:

The remainder theorem states that the remainder of dividing a polynomial f(x) by (x−a) is f(a). In our case a=−1 and f(−1)=−10.

Alternatively, using synthetic division we get the same remainder...

Here we divide −2x4−6x2+3x+1 by x+1. Note the 0 in −2,0,−6,3,1, standing for the missing x3 term's coefficient.

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