# Polynomials

## Exercise 2.5 Part 12

Question 15: Give possible expression for the length and breadth of each of the following rectangles, in which their areas are given:

(i) Area = 25a^2 - 35a + 12

Answer: Given, 25a^2 - 35a + 12

By splitting the middle term, we get:

25a^2 - 15a – 20a + 12

= 5a(5a – 3) – 4(5a – 3)

= (5a – 3)(5a – 4)

Hence, possible length = 5a – 3
Possible breadth = 5a – 4

(ii) Area = 35y^2 + 13y – 12

Answer: Given, 35y^2 + 13y – 12

By splitting the middle term, we get:

= 35y^2 + 28y – 15y – 12

= 7y(5y + 4) – 3(5y + 4)

= (5y + 4)(7y – 3)

Hence, possible length = 5y + 4
Possible breadth = 7y – 3

Question 16: What are the possible expressions for the dimensions of the cuboids whose volumes are given below?

(i) Volume: 3x^2 - 12x

Answer: Given; 3x^2 - 12x

= 3x(x – 4)

We know that, volume = length x breadth x height

Hence, possible length = 3
Possible breadth = x
Possible height = (x – 4)

(ii) Volume: 12ky^2 + 8ky – 20k

Answer: Given: 12ky^2 + 8ky – 20k

By taking 4k as common, we get:

= 4k(3y^2 + 2y – 5)

By splitting the middle term, we get:
4k(3y^2 - 3y + 5y – 5)

= 4k[3y(y – 1) + 5(y – 1)]

= 4k((y – 1)(3y + 5)

We know that volume = length x breadth x height

Hence, possible length = 4k
Possible breadth = (y – 1)
Possible height = (3y + 5)