Question

(2x^3 -3x^2 +4x -1) /(x+2)

Answer 1

`\blue{\huge {\mathrm{DIVIDING \; POLYNOMIALS}}}`

`\\`

`{===========================================}`

`{\underline{\huge \mathbb{Q} {\large \mathrm {UESTION : }}}}`

• 
  `\sf ((2x^3 -3x^2 +4x -1))/((x+2))`

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`{\underline{\huge \mathbb{A} {\large \mathrm {NSWER : }}}}`

• Through the computations performed, we came to the conclusion that the quotient is
  `\blue{\bold{2x^2 - 7x + 18}}` and the remainder is
  `\red{\bold{-37}}`.

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`{\underline{\huge \mathbb{S} {\large \mathrm {OLUTION : }}}}`

`\qquad\begin{aligned}\sf \blue{2x^2 - 7x + 18} \:\:\:\:\:\:\:\:\:\: &\\\sf x + 2 \: \: ) \overline{2x^3 - 3x^2+4x-1} \quad&\\\sf \: \: \underline{ - 2x^3 - 4x^2 \qquad\qquad \: \: \: \: } \\\sf - 7x^2 + 4x \qquad \: \: \: \\\sf \:\:\: \underline{ - 7x^2 + 14x \qquad \: } \\ \sf 18x - 1 \: \: \: \\ \underline{ \sf{ - 18x - 36 \: }} \\ \sf \red{ - 37} \end{aligned}`

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`- \large\sf\copyright \: \large\tt{AriesLaveau}\large\qquad\qquad\qquad\qquad\qquad\qquad\tt 04/02/2023`

Answer 2

Quotient ➔ 2x² - 7x + 18

Remainder ➔ - 37

━━━━━━━━━━━━━━━━━━━━━━

SolutioN ::

ㅤ

• ➸ Attachment

`\begin{gathered} \\ \\ \qquad{\rule{120pt}{7pt}} \\ \\ \end{gathered}`

VerificatioN ::

ㅤ

• ➸ Taking the product of Divisor and Quotient as LHS

`\begin{gathered} \\ \\ \; \; :\longmapsto \; \sf {x(2x^(2) - 7x + 18) + 2(2x^(2) - 7x + 18) + ( - 37)} \\ \\ \end{gathered}`

`\begin{gathered} \\ \; \; :\longmapsto \; \sf {2x^(3) - 7x^(2) + 18x + 4x^(2) - 14x + 36 - 37} \\ \\ \end{gathered}`

`\begin{gathered} \\ \; \; :\longmapsto \; \sf {2x^(3) - 7x^(2) + 4x^(2) + 18x - 14x - 1} \\ \\ \end{gathered}`

`\begin{gathered} \\ \; \; :\longmapsto \; \sf \pink{2x^(3) - 3x^(2) + 4x - 1} \\ \\ \end{gathered}`

• ➸ Taking Dividend as RHS

`\begin{gathered} \\ \\ \; \; :\longmapsto \; \sf \pink{2x^(3) - 3x^(2) + 4x - 1} \\ \\ \end{gathered}`

`\begin{gathered} \\ \; \; :\longmapsto \; \sf {LHS = RHS} \\ \\ \end{gathered}`

`\begin{gathered} \\ \; \; :\longmapsto \; \underline{\boxed{\sf{Verified}}} \; \pmb{\red{\bigstar}} \\ \\ \end{gathered}`

`\begin{gathered} \\ {\underline{\rule{150pt}{10pt}}} \end{gathered}`