How do you use synthetic division to divide #x^3+8x^2-3x+16# by #(x^2 + 5)#?

1 Answer
Jul 24, 2015

Answer:

# color(red) ((x^3+8x^2-3x+16)/(x^2+5) = x + 8 – (8x+24)/(x^2+5))#

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 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+8-(8x+24)/(x^2+5)#.

Check:

#(x^2+5)( x+8-(8x+24)/(x^2+5)) =(x^2+5)( x+8) –(8x+24) = x^3+8x^2+5x+40-8x-24 = x^3+8x^2-3x+16#