Start by setting synthetic division up:
6 | 3 5 6
Bring the 3 down,
6 | 3 5 6
3
Multiply, rinse and repeat:
6 | 3 5 6
18 138
3 23 144
Separate one term from the right, since this is vanilla synthetic division:
6 | 3 5 6
18 138
3 23 || 144
Use the appropriate polynomial rules to build your equation from there:
3x + 23 + (144/x+6)
As for the quotient I would assume it is referring to the remainder, which is 144/x+6, but that is probably a better thing for you to decide than me.
Answer:
4x^2 -27x +167
Step-by-step explanation:
(4x^3-3x^2+5x+6)/(x+6)
WE use synthetic division
x+6 =0 , so x=-6
We divide by -6. Write the coefficient of all terms inside and -6 outside.
Take down 4 as it is. then multiply the bottom number with -6 and put it in the middle. Continue the process.
-6 4 -3 5 6
-24 162 -1002
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4 -27 167 -996 (remainder)
Quotient is 4x^2 -27x +167
Remainder is -996
