How do you use synthetic division to divide #x^4-3x^3+3x^2-2x+3# by #x^2-3x+2#?

1 Answer
Jul 24, 2015

Answer:

#color(red)((x^4-3x^3+3x^2-2x+3)/(x^2-3x+2) = x^2+1+(x+1)/(x^2-3x+2)#

Explanation:

Step 1. Write only the coefficients of #x# in the dividend inside an upside-down division symbol.

1

Step 2. Negate the coefficients in the divisor and put every coefficient but the first one diagonally at the left.

2

Step 3. Drop the first coefficient of the dividend below the division symbol.

3

Step 4. Multiply the drop-down by the divisor, and put the result diagonally in the next columns.

4

Step 5. Add down the column.

5

Step 6. Repeat Steps 4 and 5 until you would go past the entries at the top with the next diagonal.

6

The quotient is #x^2+1+(x+1)/(x^2-3x+2)#.

Check:

#(x^2-3x+2)( x^2+1+(x+1)/(x^2-3x+2)) = (x^2-3x+2)( x^2+1) +x+1 = x^4-3x^3+2x^2+x^2-3x+2+x+1 = x^4-3x^3+3x^2-2x+3#