Question

find the remainder when 4x^3- 3x^2+2x-4 is divisible by x+2​

Answer 1

${ \bold{ \huge{ \red{ \green{ \mathbb{ \underline{ANSWER} : - }}}}}} \\ \\ \\ { \bold{ \underline{Given} : - }} \\ \\ { \bold{ \blue{ \: \: \: \: \: \: . \: \: a \: \: polynomial \: \: 4 {x}^{3} - 3 {x}^{2} + 2x - 4 = 0}}} \\ \\ { \bold{ \blue{ \: \: \: \: \: \: . \: \: polynomial \: \: divided \: \: by \: \: x + 2}}} \\ \\ { \bold{ \underline{ To \: \: find } : - }} \\ { \bold{ \red{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: remainder}}} \\ \\ \\ { \bold{ \orange{ \huge{ \mathfrak{ \underline{solution} : - }}}}} \\ \\ \\ { \bold { \blue{ \: \: \: \: \: \: \: \: \: \: . \: \: \: to \: \: find \: \: remainder \: \: we \: have \: \: to \: \: put}}} \\ { \bold { \blue{ \: \: \: \: \: \: \: \: \: \: \: \: \: \:x = - 2 \: \: in \: \: polynomial \: . }}} \\ \\ { \bold { \blue{ \implies \: let \: \: p(x) = 4 {x}^{3} - 3 {x}^{2} + 2x - 4}}} \\ \\ \\ { \bold { \blue{ \implies \:p( - 2) = 4 {( - 2)}^{3} - 3 {( - 2)}^{2} + 2( - 2) - 4}}} \\ \\ \\ { \bold { \blue{ \implies \: p( - 2) = 4( - 8) - 3(4) - 4 - 4}}} \\ \\ \\ { \bold { \blue{ \implies \: p( - 2) = - 32 - 12 - 8 = - 52}}} \\ \\ \\ \\ { \bold { \red{ \huge{ \: { \boxed{ \mathbb{REMAINDER = - 52}}}}}}}$