Question

find the LCM of the following (x^ -27) ( x-3)^ (x^-9) ​

Answer 1

Step-by-step explanation:

We know that LCM is the least common multiple.

Factorise 10x

3

+6x

2

−28x as follows:

10x

3

+6x

2

−28x=2x(5x

2

+3x−14)=2x(5x

2

+10x−7x−14)

=2x[5x(x+2)−7(x+2)]=2x(5x−7)(x+2)

Now, factorise 9x

3

+15x

2

−6x as follows:

9x

3

+15x

2

−6x=3x(3x

2

+5x−2)=3x(3x

2

+6x−x−2)=3x[3x(x+2)−1(x+2)]=3x(3x−1)(x+2)

Therefore, the least common multiple between the polynomials 10x

3

+6x

2

−28x and 9x

3

+15x

2

−6x is:

LCM=2×3×x×(x+2)×(3x−1)×(5x−7)=6x(x+2)(3x−1)(5x−7)

Hence, the LCM is 6x(x+2)(3x−1)(5x−7)