Question

an expression for the area of a rectangular piece of sheet metal is X^2+8x+12.
An expression for the length of the same piece of sheet metal is x+6.
Determine an expression for the width.

Answer 1

$\text{Area of rectangle} = \text{Length} \times \text{Width}\\\\\\\implies \text{Width} = \dfrac{\text{Area of reactangle}}{\text{Length}} = \dfrac{x^2 +8x +12}{x+6} = \dfrac{x^2 + 6x +2x +12}{x+6}\\\\\\\\ = \dfrac{x(x+6) +2(x+6)}{x+6}=\dfrac{(x+6)(x+2)}{x+6} = x+2$