Question

on dividing 3x^3+x^2+2x+5 by a polynomial g(x) the quotient and remainder are 3x-5 and 9x+10 respectively find g(x)​

Answer 1

Step-by-step explanation:

Here, Dividend = 3x³+x²+2x+5

Quotient = g(x)

Remainder = 9x+10

Divisor = 3x-5

Dividend = Quotient × Divisor + Remainder

Quotient = Dividend / Divisor + Remainder

Therefore,

g(x) = Quotient

Further, you can solve..

Answer 2

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \large\fcolorbox{teal}{lavenderblush}{Question⋆᭄᭄}$

ᴏɴ ᴅɪᴠɪᴅɪɴɢ 3x³+x²+2x+5 ʙʏ ᴀ ᴘᴏʟʏɴᴏᴍɪᴀʟ g(x) ᴛʜᴇ ǫᴜᴏᴛɪᴇɴᴛ ᴀɴᴅ ʀᴇᴍᴀɪɴᴅᴇʀ ᴀʀᴇ 3x-5 ᴀɴᴅ 9x+10 ʀᴇsᴘᴇᴄᴛɪᴠᴇʟʏ ғɪɴᴅ g(x)

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \large\fcolorbox{teal}{lavenderblush}{Ꭺnѕwєr⋆᭄᭄}$

$\bf \green{ 『 \: By \: using \: division \: rule ,we \: have \: 』 }\\\sf \blue{ Dividend = Quotient × Divisor + Remainder}$

$\sf\therefore \: 3 {x}^{3} + {x}^{2} + 2x + 5 \\ \sf= (3x - 5)g(x) + 9x$

$\sf\implies \: 3 {x}^{3} + {x}^{2} + 2x + 5x - 9x - 10 \\ \sf = (3x - 5)g(x)$

$\sf\implies \: 3 {x}^{3} + {x}^{2} - 7x - 5 \\ \sf = (3x - 5)g(x)$

$\large\rightarrow \sf \: \frac{g(x) = 3 {x}^{3} + {x}^{2} - 7x - 5 }{3x - 5}$

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3x - 5 ) 3x³ + x² - 7x + 5( x² + 2x + 1

           3x³ - 5x

         -------------------------

              6x² -  7x  -  5

              6x²  - 10x

          --------------------------

                           3x - 5⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀3x - 5

⠀⠀⠀⠀⠀--------------------------

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀x

$\large \bf \blue{\therefore }\green{ g(x) = {x}^{2} + 2x + 1}$

     

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