Question

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

Answer 1

Answer:

Option C.

Step-by-step 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

$\dfrac{6x^3+x^2-3}{x-7}$

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.