Question

(x^3+3x^2+5x+3) divided by (x+1)

Answer 1

ㅤㅤ [ ATTACHMENT ]

• ➸ Quotient = x² + 2x + 3
• ➸ Remainder = 0

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VerificatioN ::

• ➸ LHS = Multiplying the (Divisor = x + 1) with the quotient

ㅤ

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

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

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

`\begin{gathered} \\ \; \; :\longmapsto \; \sf {x^(3) + 3x^(2) + 5x + 3} \\ \\ \end{gathered}`

• ➸ RHS = Dividend

ㅤ

`\begin{gathered} \\ \; \; :\longmapsto \; \sf {x^(3) + 3x^(2) + 5x + 3} \\ \\ \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{\pmb{\rule{170pt}{4pt}}}} \end{gathered}`