Question

find the qoutient and remainder when 6x⁴+11x³+13x²-3x+27 is divided by 3x+4. verify the answer with remainder thorem

Answer 1

For the remainder theorem we generally use synthetic division.

If (x+2) is a factor of P(x) then x=-2 will be a zero of P(x)

 

we have P(x) = 2x2-3x+4

The coefficients in descending order from the variable with the highest

exponent to the constant are 2, -3, 4

 

Write the -2 on the left with a diagonal separating it from the coefficients:

 

-2 / 2    -3     4        1)bring down the first coefficient (2)

            -4   14         2)multiply that by the -2 giving -4
        3)bring that product up under the next coefficient

       2   -7   18            add down    4 Repeat to the end.  Last number is the remainder
The remainder is 18.  The remainder theorem says that f(-2)
The polynomial we get when we divide is

(2x2 -3x+4)/(x+2)= 2x-7+ 18/(x+2)