How do you divide #2x^3 + 6x^2 - 2x - 5# by #x + 3# using synthetic division?

1 Answer
Jan 11, 2016

Answer:

#(2x^3+6x^2-2x-5) div (x+3) = 2x^2-2 1/(x+3)#

Explanation:

#(color(blue)(2)x^3color(blue)(+6)x^2color(blue)(-2)xcolor(blue)(+3)) div (xcolor(red)(+)color(green)(3))#

would be set-up for synthetic division as:

#{: (,"|",color(white)("X")color(blue)(2),color(blue)(+6),color(blue)(-2),color(blue)(-5)), (,"|",,,,), (bar(xx (color(red)(-)color(green)(3))),"|",bar(color(white)("X")color(orange)(2)color(white)("X")),bar(color(white)("XX")),bar(color(white)("XX")),bar(color(white)("XX"))) :}#

For each column
- write the product of #(-3)# and the bottom entry of the previous column on the second line of the next column.
- add the entries in the next column to get the bottom line value for the next column.

#{: (,"|",color(white)("X")color(blue)(2),color(blue)(+6),color(blue)(-2),color(blue)(-5)), (,"|",,-6,color(white)("X")0,color(white)("X")6), (bar(xx (color(red)(-)color(green)(3))),"|",bar(color(white)("X")color(orange)(2)color(white)("X")),bar(color(white)("X")color(orange)(0)),bar(color(orange)(-2)),bar(color(white)("X")color(cyan)(1))) :}#

The last entry in the bottom line (#color(cyan)(1)#) is the remainder.
The preceding entries are the coefficients of the quotient expression: (#color(orange)(2)x^2color(orange)(+0)xcolor(orange)(-2)#)