Find the LCM for
u^3 + 6u^2 + 9u, u^2 - 6u
I came up with
u(u+3)(u-6) is this correct?
The factors of the first term are
u(u^2 + 6u + 9) = u(u+3)^2
and of the second term are
u(u-6)
The LCM is u*(u+3)^2*(u-6)
u+3 must appear twice.
To find the least common multiple (LCM) of the given polynomials, we need to factorize each polynomial completely and then find the product of all the unique factors raised to their highest power.
Let's factorize the polynomials:
1. u^3 + 6u^2 + 9u
= u(u^2 + 6u + 9)
= u(u + 3)(u + 3)
= u(u + 3)^2
2. u^2 - 6u
= u(u - 6)
Now, we will find the LCM by multiplying all the unique factors raised to their highest power.
The unique factors are: u, (u + 3), (u - 6)
u's highest power: 1 (from u)
(u + 3)'s highest power: 2 (from (u + 3)^2)
(u - 6)'s highest power: 1 (from (u - 6))
Therefore, the LCM is:
u(u + 3)^2(u - 6)