Answer:
The quotient= [tex]4x^2-27x+167[/tex].
Step-by-step explanation:
Given
Dividened= [tex]4x^3-3x^2+5x+6[/tex]
Divisor=[tex]x+6[/tex]
In synthetic division : Put denomerator is equal to zero.
Put x+6=0
x=-6
Put -6 in division box as a divisor.
Coefficient of x^3=4
Coefficient of x^2=-3
Coefficient of x=5
Constant value=6
Put the coefficient of x^3,x^2,x and constant in descending order of power of x in division problem.
Now ,bring the coefficient of x^3 is 4 straight down .
Now, multiply the numbe -6 in the division box with the number 4 brought down and put the result -24 below the number - 3 of next column.
By adding we get -27 and write result in the bottom of row .
Again ,the number -6 multiply with -27 and put the result=162 below the number of next column.
By adding two number together we get 167 and put the result in the bottom of row.
Again, the number -6 in division box multiply with the number 167 and put the result=1002 below the number of next column.
Adding two number together we get 1008 and write in the bottom of row.
Last number is remainder and then write the remainder in fraction .
In quotient the power of x reduces by 1 from the numertor.
Hence, the quotient =[tex]4x^2-27x+167[/tex]
Remainder=[tex]\frac{1008}{x+6}[/tex].
