Question

LCM of x²+5x+6 and x²-x-6 is ………………………

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Answer 1

`(x^2 - 9)(x + 2)`

Explanation:

Given:

`x^2 + 5x + 6`

`x^2 - x - 6`

Required:

LCM of the polynomials

SOLUTION:

Step 1: Factorise each polynomial

`x^2 + 5x + 6`

`x^2 + 3x + 2x + 6`

`(x^2 + 3x) + (2x + 6)`

`x(x + 3) + 2(x + 3)`

`(x + 2)(x + 3)`

`x^2 - x - 6`

`x^2 - 3x +2x - 6`

`x(x - 3) + 2(x - 3)`

`(x + 2)(x - 3)`

Step 2: find the product of each factor that is common in both polynomials.

We have the following,

`x^2 + 5x + 6 = (x + 2)(x + 3)`

`x^2 - x - 6 = (x + 2)(x - 3)`

The common factors would be: =>

`(x + 2)` (this is common in both polynomials, so we would take just one of them as a factor.

`(x + 3)` and,

`(x - 3)`

Their product =
`(x - 3)(x + 3)(x +2) = (x^2 - 9)(x + 2)`