The correct option is d which is -6 | 8 +1 +0 -5.
Given to us,
[tex]\dfrac{(8x^3 + x^2-5)}{(x-6)}[/tex]
We need synthetic division form,
Synthetic division is a method of shorthand, or shortcut, to divide a polynomial when it has to be divided by a linear factor.
For this, [tex]\dfrac{(8x^3 + x^2-5)}{(x-6)}[/tex]
we can write [tex]\dfrac{(8x^3 + x^2+0x-5)}{(x-6)}[/tex],
Now,
[tex](8x^3 + x^2+0x-5) \div (x-6)[/tex]
For, synthetic division, writing only the coefficient in the basic format,
[tex]\bold{(8x^3 + x^2+0x-5) \rightarrow}[/tex] 8 +1 +0 -5
[tex]\bold{ (x-6)\rightarrow}[/tex] -6
Therefore, when writing in Synthetic division form -6 | 8 +1 +0 -5.
Hence, the correct option is d which is -6 | 8 +1 +0 -5.
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