103 The Division Algorithm  What you know…  a Review of Long division24148122240101412282440.03640! .210 32Now we move on to Polynomial Division  "#$#)()(xvxu)()()( xvxwxu=0)(&0)(==xvxuIf u(x) = x3+ x & v(x) = x2+ x + 1)(123xwxxxx=+++Previous Long Divisonxxxx +++321xx3+ x2+xx+-x2+0-1-x2-x- 1+x2+x+1x+1remainder3Lets take it back to the book defn)1)((23++=+ xxxwxx)()()( xvxwxu=Think about w(x)   "  %)1)((23++=+ xxxwxx)()()( xvxwxu=w(x) must be degree 1&  "&' "(& '  "4Now Substitute: w(x) = ax+b )1)((23+++=+ xxbaxxx)()()( xvxwxu=bbxbxaxaxax +++++=223Now Substitute: w(x) = ax+b )1)((23+++=+ xxbaxxx)()()( xvxwxu=bbxbxaxaxax +++++=223))Now Substitute: w(x) = ax+b (bbxbxaxaxax +++++=223)1)((23+++=+ xxbaxxx)()()( xvxwxu=bxbaxbaax +++++= )()(235Remember –this is suppose to = w(x)bxbaxbaaxxx +++++=+)()(233&*"&*+&*"&*+So, think about this…,",+,",+bxbaxbaaxxx +++++=+ )()(233" +" +-./So, think about this…,",+,",+bxbaxbaaxxx +++++=+ )()(233" +" +0," +1 -2 6Manipulate    )()()( xvxwxu= ' remainderxvofmultiplexu+=)(..)(Manipulate2  ,"3,+ ",+, "remainderxvofmultiplexu+=)(..)(bxbaxbaaxxx +++++=+ )()(233"+" +The goal - ax+b(from slide 9),", ","4 "   remainderxvofmultiplexu+=)(..)(remainderxvxxu+−=)()1()(7So w(x) = x-1  (5* '*)1)(1()()(2++−= xxxxvxw1)()(3−= xxvxwxxxvxwxu +==3)()()(Manipulate %  "*'6*7xx +313−x*xx +−13113++− xx  Put it all together1)1)(1()1()1()(233++++−=++−=+= xxxxxxxxxu+)()( xvxwremainder1)1)(1(23++++−=+ xxxxxx)1()1(32−+++xxxxx1++xremainder8Previous Long Divisonxxxx +++321xx3+ x2+xx+-x2+0-1-x2-x- 1x+1remainderx+1Switch gears – Think about degrees&* &    &    0   )()()()( xrxvxqxu+=simplify matters remove the (x)rqvu+=, *  ','*, *, 93.1 Repeated Addition* 8$9*  2)(2++= xxxv12)(3−+= xxxu)()()( xvxqxu−)()(xvxu1)()1()(+=−−xxvxxuSame work in a new format…   *#  123−+ xx:*22++ xx   *#     *#  Same work in a new format…   *#  '    123−+ xx:*22++ xx1−x1+x   *#  '       *#  '