question #4

Question

Use synthetic division to find the quotient and remainder when the first polynomial is divided by the second.

x^4-7,x-1

The quotient is __.

The remainder is __.

 

help is greatly appreciated, thank you!

Answer 1

(x⁴ - 7) / (x - 1)

 

 

The method divides the coefficient of the dividend by the possible root.  That possible root is found in the divisor.   We set up the division like this.

 

 

1  |  1     0     0      0      -7

 

              1     1      1       1

________________________

    

       1     1     1      1      -6

 

 

 

Quotient = x³ + x² + x + 1

Remainder = -6

 

Explanation of what just happened in the process:

 

I brought down the first coefficient below the line.  I then multiplied that number by the divisor.  The product became the addend in the second column.  I added the numbers in the second column and placed the sum below the line, in that column.  I multiplied the sum by the divisor, and the product became the addend in the next column.  I then repeated the steps until I got to the last coefficient.

 

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