Question

A mason uses the expression x² + 6x + 8 to represent the area of the floor of a room. If the decides that the length of the room will be represented by (x + 4), what will the width of the room be in terms of x?

Answer 1

Given length of the room = x + 4 

Area of the room = x² + 6x + 8

Length × breadth = x² + 6x + 8

breadth = `(x^2 + 6x + 8)/(x + 4)`  ...(1)

Factorizing x² + 6x + 8, it is in the form of ax² + bx + c

Where a = 1, b = 6, c = 8

The product a × c = 1 × 8 = 8

sum = b = 6

Product = 8	Sum = 6
1 × 8 = 8	1 + 8 = 9
2 × 4 = 8	2 + 4 = 6

The middle term 6x can be written as 2x + 4x

∴ x² + 6x + 8 = x² + 2x + 4x + 8

= x(x + 2) + 4(x + 2)

x² + 6x + 8 = (x + 2)(x + 4)

Now from (1)

breadth = `(x^2 + 6x + 8)/(x + 4)`

= `((x + 2)(x + 4))/((x + 4))`

= x + 2

∴ Width of the room = x + 2