Question

A contractor uses the expression 4x² + 11x + 6 to determine the amount of wire to order when wiring a house. If the expression comes from multiplying the number of rooms times the number of outlets and he knows the number of rooms to be (x + 2), find the number of outlets in terms of ’x’. [Hint : factorise 4x² + 11x + 6]

Answer 1

Given Number of rooms = x + 2

Number of rooms × Number of outlets = amount of wire.

(x + 2) × Number of outlets = 4x² + 11x + 6

Number of outlets = `(4x^2 + 11x + 6)/(x + 2)` ...(1)

Now factorising 4x² + 11x + 6 which is of the form ax² + bx + c with a = 4, b = 11, c = 6.

The product a × c = 4 × 6 = 24

sum b = 11

Product = 24	Sum = 11
1 × 24 = 24	1 + 24 = 25
2 × 12 = 24	2 + 12 = 14
3 × 8 = 24	3 + 18 = 11

The middle term 11x can be written as 8x + 3x

∴ 4x² + 11x + 6 = 4x² + 8x + 3x + 6

= 4x(x + 2) + 3(x + 2)

4x² + 11x + 6 = (x + 2)(4x + 3)

Now from (1) the number of outlets

= `(4x^2 + 11x + 6)/(x + 2)`

= `((x + 2)(4x + 3))/((x + 2))`

= 4x + 3

∴ Number of outlets = 4x + 3