Division of Algebraic Expressions

Example 1

$$ (x^2+8x+12)÷(x+6) $$

Solution

$$ \begin{array}{r} x+2\phantom{xxxxxx} \\ x+6{\overline{\smash{\big)}\,x^2+8x+12\phantom{x}}}\\ \underline{-(x^2+6x)\phantom{xxxx}}\\ 2x+12\phantom{x}\\ \underline{-(2x+12)}\phantom{}\\ 0\phantom{x} \end{array}\ $$

Example 2

$$ (x^2+9x+20)÷(x+4) $$

Solution

$$ \begin{array}{r} x+5\phantom{xxxxxx}\\ x+4{\overline{\smash{\big)}\,x^2+9x+20\phantom{x}}} \\ \underline{-(x^2+4x)\phantom{xxxx}} \\ 5x+20\phantom{x} \\ \underline{-(5x+20)}\phantom{} \\ 0\phantom{x} \end{array} $$

Example 3

$$ (x^2+7x-60)÷(x-5) $$

Solution

$$ \begin{array}{r} x+12\phantom{xxxxxx}\\ x-5{\overline{\smash{\big)}\,x^2+7x-60\phantom{x}}} \\ \underline{-(x^2-5x)\phantom{xxxx}} \\ 12x-60\phantom{x} \\ \underline{-(12x-60)}\phantom{} \\ 0\phantom{x} \end{array} $$

Example 4

$$ (x^2-18x+80)÷(x-8) $$

Solution

$$ \begin{array}{r} x-10\phantom{xxxxxx}\\ x-8{\overline{\smash{\big)}\,x^2-18x+80\phantom{x}}} \\ \underline{-(x^2-8x)\phantom{xxxxx}} \\ -10x+80\phantom{x} \\ \underline{-(-10x+80)}\phantom{} \\ 0\phantom{x} \end{array} $$