What is the LCM of the following polynomials: 3x^2 -18x +27, 2x^3 -4x^2 -6x?

Ans. 6x(x+1)(x-3)^2

3x^2-18x+27=

3(x-3)^2

2x^3-4x^2-6x=

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

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

=>

LCM=6x(x+1)(x-3)^2

or

LCM=6x^4-30x^3+18x^2+54x

3 x² - 18x + 27 = 3 [ x² - 6x + 9 ]

3 x² - 18x + 27 = 3 [ x - 3 ] ²

2x³ - 4x² - 6x = [ 2x ] [ x² - 2x - 3 ]

2x³ - 4x² - 6x = [ 2x ] [ x - 3 ] [ x + 1 ]

The given polynomials:

3x^2 - 18x + 27 = 3(x^2 - 6x + 9) = 3(x - 3)^2

2x^3 - 4x^2 - 6x = 2x(x^2 - 2x - 3) = 2x(x - 3)(x + 1)

The LCM of the polynomials:

6x(x - 3)^2(x + 1) = 6 x^4 - 30 x^3 + 18 x^2 + 54 x

3x^2 - 18x + 27 = 3(x^2 - 6x + 9) = 3(x-3)^2.

2x^3 - 4x^2 - 6x = (2x)(x^2 - 2x - 3) = (2x)(x-3)(x+1).

The LCM is (6x)(x+1)(x-3)^2 .

Factor each:

3(x^2 - 6x + 9) = 3(x - 3)(x - 3)

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

so you need a 3, a 2x, two (x - 3)'s and one (x + 1): 3•2x•(x - 3)(x - 3)(x + 1)

1

do your own homework

3 and 2x