Question 1129057
{{{(3x^4-2x^2+2)/(x-1/4) }}}



write down the coefficients of the polynomial and put the zero from {{{x-1/4=0}}} ( {{{x=1/4}}} ) at the left


{{{1/4}}}|| {{{3}}} −−−−−−  {{{ 0 }}}−−−−−−       {{{-2}}} −−−−−−     {{{ 0}}}  −−−−−−   {{{ 2}}}


bring down the leading coefficient to the bottom row.


{{{1/4}}}|| {{{3}}} −−−−−−  {{{ 0 }}}−−−−−−       {{{-2}}} −−−−−−     {{{ 0}}}  −−−−−−   {{{ 2}}}

−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
−−−−{{{3}}}


multiply by the number on the left, and carry the result into the next column: {{{(1/4)3=3/4}}}


{{{1/4}}}|| {{{3}}} −−−−−−  {{{ 0 }}}−−−−−−      {{{ -2}}} −−−−−−     {{{ 0 }}} −−−−−−    {{{2}}}

−−−−−−−−−−−−{{{3/4}}}−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
−−−−{{{3}}}


add down the column: {{{0+3/4=3/4}}}

{{{1/4}}}|| {{{3}}} −−−−−−   {{{0}}} −−−−−−       {{{-2 }}}−−−−−−     {{{ 0}}}  −−−−−−    {{{2}}}

−−−−−−−−−−−−{{{3/4}}}−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
−−−−3−−−−−−−{{{3/4}}}


multiply by the number on the left, and carry the result into the next column: {{{(1/4)(3/4)=3/16}}}


{{{1/4}}}|| {{{3}}} −−−−−−  {{{ 0}}} −−−−−−     {{{  -2}}} −−−−−−   {{{   0}}}  −−−−−−   {{{ 2}}}

−−−−−−−−−−−−{{{3/4}}}−−−−−−−−−−{{{3/16}}}−−−−−−−−−−−−−−−−−−−−−−−−
−−−−3−−−−−−−{{{3/4}}}



add down the column: {{{-2+3/16=-29/16}}}


{{{1/4}}}|| {{{3}}} −−−−−−  {{{ 0}}} −−−−−−   {{{  -2}}} −−−−−−    {{{  0 }}} −−−−−−   {{{ 2}}}

−−−−−−−−−−−−{{{3/4}}}−−−−−−−−−−{{{3/16}}}−−−−−−−−−−−−−−−−−−−−−−−−
−−−−{{{3}}}−−−−−−−{{{3/4}}}−−−−−−−−−..{{{-29/16}}}



multiply by the number on the left, and carry the result into the next column:{{{ (1/4)(-29/16)=-29/64}}}


{{{1/4}}}|| {{{3}}} −−−−−−  {{{ 0}}} −−−−−−      {{{ -2}}} −−−−−−    {{{  0}}}  −−−−−−    {{{2}}}

−−−−−−−−−−−−{{{3/4}}}−−−−−−−−−−{{{3/16}}}−−−−−..{{{-29/64}}}−−−−−−−−−−−−−−−−−
−−−−{{{3}}}−−−−−−−{{{3/4}}}−−−−−−−−−..{{{-29/16}}}

add down the column: {{{0+(-29/64)=-29/64}}}


{{{1/4}}}|| {{{3}}} −−−−−−  {{{ 0}}} −−−−−−      {{{ -2}}} −−−−−−     {{{ 0}}}  −−−−−−    {{{2}}}

−−−−−−−−−−−−{{{3/4}}}−−−−−−−−−−{{{3/16}}}−−−−−..{{{-29/64}}}−−−−−−−−−−−−−−−−−
−−−−{{{3}}}−−−−−−−{{{3/4}}}−−−−−−−−−..{{{-29/16}}}−−−..{{{-29/64}}}


multiply by the number on the left, and carry the result into the next column: {{{(1/4)(-29/64)=-29/256}}}


{{{1/4}}}|| {{{3}}} −−−−−−  {{{ 0}}} −−−−−−     {{{  -2}}} −−−−−−     {{{ 0}}}  −−−−−−    {{{2}}}

−−−−−−−−−−−−{{{3/4}}}−−−−−−−−−−{{{3/16}}}−−−−−..{{{-29/64}}}−−−−−{{{29/256}}}−−−−−−−−−−−
−−−−{{{3}}}−−−−−−−{{{3/4}}}−−−−−−−−−..{{{-29/16}}}−−−..{{{-29/64}}}


add down the column:{{{ 2+(-29/256)=483/256}}}


{{{1/4}}}|| {{{3}}} −−−−−−  {{{ 0}}} −−−−−−     {{{  -2}}} −−−−−−     {{{ 0 }}} −−−−−−    {{{2}}}

−−−−−−−−−−−−{{{3/4}}}−−−−−−−−−−{{{3/16}}}−−−−−..{{{-29/64}}}−−−−−{{{29/256}}}−−−−−−−−−−−
−−−−{{{3}}}−−−−−−−{{{3/4}}}−−−−−−−−−..{{{-29/16}}}−−−..{{{-29/64}}}−−−−−{{{483/256}}}



{{{3x^4-2x^2+2=(3x^3+(3/4)x^2-(29/16)x-29/64)(x-1/4)+483/256}}}