Question

The volume of a cuboid is X³-7X+6 , then the longest side of the cuboid is.?

Answer 1

x^3 - 7x + 6

= x^3 - 4x - 3x + 6

= x (x^2 - 4) - 3(x-2)

= x [(x) ^2 - (2)^2] - 3(x-2)

= x (x-2)(x+2) - 3(x-2)

= (x-2) [ x (x + 2) - 3]

= (x - 2) [ x^2 + 2x - 3]

= (x-2) [ x^2 + 3x - x- 3]

= ( x - 2)[ x (x+3) - 1(x-3)]

= (x-2)(x-1)(x+3)

Sides are (x-2), (x-1) and (x+3)

Longest side = x+3

Answer 2

Answer:

Longest side of cuboid is x+3.

Step-by-step explanation:

Given volume of cuboid = x³ - 7x + 6

= x³ - 4x - 3x + 6

= x (x² - 4) - 3(x-2)

= x [x² - 2²] - 3(x-2)

∵ a² - b² = (a + b)(a - b)

= x (x+2)(x-2) - 3(x-2)

Taking (x - 2) common

= (x-2) [ x (x + 2) - 3]

= (x - 2) [ x² + 2x - 3]

= (x-2) [ x² + 3x - x- 3]

= ( x - 2)[ x (x+3) - 1(x-3)]

= (x - 2)(x - 1)(x + 3)

∵ Volume of cuboid = length × width × height

So sides of cuboid are (x - 2), (x - 1) and (x + 3)

And longest side is x+3