Question

Which of the following shows the division problem below in synthetic division form? (6x^3+x^2-3)/(x-7)

A. -7/6 1 0 -3
B. -7/6 1 -3
C. 7/ 6 1 0 -3
D. 7/6 1 -3

Answer 1

Option C.

Explanation:

If a polynomial P(x) is divided by (x-c), then we write leading coefficients inside the synthetic division line and c outside the synthetic division line.

The given division problem is

`(6x^3+x^2-3)/(x-7)`

Here,

`x-c=x-7\Rightarrow c=7`

The numerator polynomial can be written as

`P(x)=6x^3+x^2+0x-3`

So, the coefficients of numerator are 6, 1, 0, -3.

The synthetic division form for given division problem is

7 | 6 1 0 -3

Therefore, the correct option is C.