Question

Brainliest if correct! What is (2^3-2g-8)/(g-4)? (Synthetic Division)

Answer 1

Answer:

2g^2 +8g +30   + 112/(g-4)

Step-by-step explanation:

2g^3 + 0g^2 -2g -8   divide by g-4

The coefficients go on the first line and the root goes in the divisor spot

Bring down the first coefficient

      2      0     -2      -8

4

----------------------------------

    2

Multiply the root by the  number on the bottom and add to the coefficient

      2      0     -2      -8

4             8

----------------------------------

    2        8

Multiply the root by the  number on the bottom and add to the coefficient

      2      0     -2      -8

4             8      32

----------------------------------

    2        8      30

Multiply the root by the  number on the bottom and add to the coefficient

      2      0     -2      -8

4             8      32    120

----------------------------------

    2        8      30    112

Since this was a third degree polynomial, we subtract 1 from the power and we have a second degree polynomial as our answer.  The first term is the coefficient of the 2nd degree term and so on until we get to the last term which is the remainder.  We put that over the divisor.

2g^2 +8g +30   + 112/(g-4)

Answer 2

notice the great reply above, lemme post to the risk of being redundant.

notice, for a synthetic division the dividend has to be sorted in descending order, and any missing terms, are really there, but they just happen to have a coefficient of 0.

$\bf 2g^3-2g-8\div g-4\implies 2g^3+\stackrel{\downarrow }{0g^2}-2g-8\div g-4 \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{r|rrrrr} 4&2&0&-2&-8\\ &&8&32&120\\ \cline{1-5} &2&8&30&112&\leftarrow remainder \end{array}~\hspace{5em}2g^2+8g+30+\frac{112}{g-4}$