# How do you use synthetic division to divide #(4x^2 - 2x + 6) (2x - 3) ^ -1#?

##### 1 Answer

#### Explanation:

is equivalent to

Using synthetic division (note that there may be slight variations in the structure depending upon how this is being taught):

Dividend:

Divisor:

#{: (,"|",color(red)(4),color(red)(-2),color(red)(+6)), (,"|",,6,6), (,,"-----","-----","-----"), (/color(blue)(2),"|",4,4,12), (color(white)("XX")color(cyan)(+3),"|",2,2,) :}#

Note the change in the sign of the constant term of the divisor.

"Bring down" the

Divide by the

Multiply by

#{: (,"|",4,-2,+6), (,"|",,6,), (,,"-----","-----","-----"), (/2,"|",4,,), (color(white)("XX")+3,"|",2,,) :}#

Add the

Divide by the

Miultiply by

#{: (,"|",4,-2,+6), (,"|",,6,6), (,,"-----","-----","-----"), (/2,"|",4,4,), (color(white)("XX")+3,"|",2,2,) :}#

Add the

#{: (,,x^2,x^1,x^0), (,"|",4,-2,+6), (,"|",,6,6), (,,"-----","-----","-----"), (/2,"|",4,4,color(green)((12))), (color(white)("XX")+3,"|",2,2,), (,,x^1,x^0,) :}#

Note: the additional rows showing corresponding powers of#x# are not really part of the synthetic division (but hopefully add some clarity).