Advertisements
Advertisements
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?
Advertisements
Solution
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
APPEARS IN
RELATED QUESTIONS
Factorize each of the following expression:
27x2 − 12y2
Factorize each of the following expression:
12m2 − 27
Factorize each of the following expression:
144a2 − 169b2
Factorize each of the following expression:
a4 − 16b4
Factorize each of the following expression:
x8 − 1
Factorize each of the following expression:
a4b4 − 81c4
Factorize each of the following quadratic polynomials by using the method of completing the square:
p2 + 6p − 16
Factorize each of the following quadratic polynomials by using the method of completing the square:
x2 + 12x + 20
Factorize each of the following quadratic polynomials by using the method of completing the square:
z2 − 4z − 12
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]
