Question

Divide:2x^3+9x^2+10x+3 by 2x+1

Answer 1

`(2x^3+9x^2+10x+3)/(2x+1)`

start rewriting the square term and the linear term

`(2x^3+2x^2+7x^2+7x+3x+3)/(2x+1)`

take the common factor

`(2x^2(x+1)+7x\cdot(x+1)+3\cdot(x+1))/(2x+1)`

factor the expression

`((x+1)\cdot(2x^2+7x+3))/(2x+1)`

rewrite the expression

`((x+1)\cdot(2x^2+6x+x+3))/(2x+1)`

take common factor

`((x+1)\cdot(2x(x+3)+x+3))/(2x+1)`

factor the expression

`((x+1)\cdot(x+3)(2x+1))/(2x+1)`

simplify

`\begin{gathered} (x+1)(x+3) \\ x^2+x+3x+3 \\ x^2+4x+3 \end{gathered}`