how do you do this on divide using synthetic division(k^4+3k^3-14k^2-11k+54)÷(k+5)

Question

How do you show work for divide using synthetic division(k^4+3k^3-14k^2-11k+54)÷(k+5)

Answer 1

We divide the coefficients of the dividend by the possible root of the dividend.  Since we are dividing by (x + 5), the possible root is -5.  This is also the divisor.

 

We set up the division.

 

 

-5 | 1     3     -14     -11      54

 

            -5      10      20      -45

__________________________

      1    -2      -4       9         9

 

 

The quotient is  x³ - 2x² - 4x + 9

The remainder is 9

 

 

An explanation of the process:

 

Bring down the first coefficient under the line.  Then multiply that number by the divisor.  The product becomes the addend in the second column.  Then add the numbers in the second column.  Place the sum in that same column.  Multiply that sum by the divisor.  The product becomes the addend in the next column.  Repeat the steps until you get to the last coefficient.

 

The number under the line are the coefficients of the quotient, with the last digit being the remainder.