Question

divide the polynomial p(x) = 2x²+3x+1 by (x+2) and write quotient and remainder ​

Answer 1

Step-by-step explanation:

the quotient will be 2x + 1

and remainder will be 1

I did it mentally so I can't sure that I am rgt...

but still pls mark me as the brainliest.....and follow me :)

Answer 2

Answer :

• Quotient = 2x - 1
• Remainder = 3

Step-by-step explanation :

Dividing the polynomial p(x) = 2x² + 3x + 1 by (x + 2)

$\implies \frac{2x^2+3x+1}{x+2}$

• The number which we divide is dividend and the number by which we divide is divisor.

      Dividend = 2x² + 3x + 1

      Divisor = x + 2

Step - 1 :

Divide the first term of the dividend by the first term of the divisor. Then we get the first term of the quotient.

   $\bf \frac{2x^2 \leftarrow \text{[first term of dividend]}}{x\leftarrow \text{[first term of divisior]}} =2x \leftarrow \text{[first term of quotient]}$

            $\sf\Large\qquad\qquad2x\\ \begin{array}{cc} \cline{2 - 2}\sf x+2)&\sf \ 2x^2+3x+1\\ \end{array}$

Step - 2 :

Multiply the divisor (x + 2) by 2x

  $(x+2) \times 2x =2x^2+4x$

       $\sf\Large\qquad\qquad2x\\ \begin{array}{cc} \cline{2 - 2}\sf x+2)&\sf \ 2x^2+3x+1\\&\sf 2x^2+4x \ \ \ \ \end{array}$

Step - 3 :

Subtract (2x² + 4x) from 2x² + 3x

   =  2x² + 3x - (2x² + 4x)

   =  2x² + 3x - 2x² - 4x

   =  -x

     $\sf\Large\qquad\qquad \ \ \ \ 2x\\ \begin{array}{cc} \cline{2 - 2}\sf x+2 )&\sf \ 2x^2+3x+1\\ \text{subtract:}&\sf2x^2+4x \ \ \ \ \\ \cline{2-2}& \sf \ \ \ \ -x} \end{array}$

Step - 4 :

Bring down the next term, 1

     $\sf\Large\qquad\qquad \ \ \ \ 2x\\ \begin{array}{cc} \cline{2 - 2}\sf x+2 )&\sf \ 2x^2+3x+1\\ \text{subtract:}&\sf \ 2x^2+4x \ \ \ \downarrow \\ \cline{2-2}& \sf \ \ \ \ \ \ \ -x+1} \end{array}$

Step - 5 :

Divide -x by x to get the second term of the quotient

    $\bf \frac{-x}{x} =-1$

     $\sf\Large\qquad\qquad \ \ \ \ 2x-1\\ \begin{array}{cc} \cline{2 - 2}\sf x+2 )&\sf \ 2x^2+3x+1\\\text{subtract:}&\sf \ 2x^2+4x \ \ \ \downarrow\\ \cline{2-2}& \sf \ \ \ \ \ \ \ -x+1 \end{array}$

Step - 6 :

Multiply the divisor by -1

(x + 2) (-1) = -x - 2

    $\sf\Large\qquad\qquad \ \ \ \ 2x-1\\ \begin{array}{cc} \cline{2 - 2}\sf x+2 )&\sf \ 2x^2+3x+1\\\text{subtract:} &\sf \ 2x^2+4x \ \ \ \downarrow\\ \cline{2-2}& \sf \ \ \ \ \ \ \ -x+1\\ &\sf \ \ \ \ \ \ \ -x-2 \end{array}$

Step - 7 :

Subtract -x-2 from -x+1

   = (-x + 1) - (-x - 2)

   = -x + 1 + x + 2

   = 3

   $\sf\Large\qquad\qquad \ \ \ \ 2x-1\\ \begin{array}{cc} \cline{2 - 2}\sf x+2 )&\sf \ 2x^2+3x+1\\\text{subtract:}&\sf \ 2x^2+4x \ \ \ \downarrow\\ \cline{2-2}& \sf \ \ \ \ \ \ -x+1\\ \text{subtract:}&\sf \ \ \ \ \ \ -x-2 \\ \cline{2-2} & \sf \ \ \ \ \ \ \ \ \ \ \ \ \ 3 \\ \cline{2-2} \end{array}$

• Quotient = 2x - 1
• Remainder = 3