Division of Algebraic Expressions

Ex: 1) Divide $6x^3$ by $2x$

Sol:

$\frac{6x^3}{2x} = 3x^2$

2) Divide $-20x^4$ by $10x^2$

Sol:

$\frac{-20x^4}{10x^2} = -2x^2$

3) Divide $7x^2y^2z^2$ by $14xyz$

Sol:

$\frac{7x^2y^2z^2}{14xyz} = \frac{xyz}{2}$

Ex: 1) Divide $24(x^2yz + xy^2z + xyz^2)$ by $8xyz$

Sol:

$\frac{24(x^2yz + xy^2z + xyz^2)}{8xyz}$

$\quad \quad = \frac{24xyz(x+y+z)}{8xyz}$

$\quad \quad = \mathbf{3(x+y+z)}$

Ex: 2) Divide $3y^8 - 4y^6 + 5y^4$ by $y^4$

Sol:

$\frac{3y^8 - 4y^6 + 5y^4}{y^4}$

$\quad \quad = \frac{\cancel{y^4}(3y^4 - 4y^2 + 5)}{\cancel{y^4}}$

$\quad \quad = \mathbf{3y^4 - 4y^2 + 5}$

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