Answer :
We need Factorize each polynomial completely and Identify the highest power of each unique factor. The LCM is the product of the highest power of each unique factor.the LCM of the given polynomials is[tex](5x^2 - x)(x^4).[/tex]
To find the least common multiple (LCM) of the given polynomials, we need to first factorize each polynomial completely.
The given polynomials are:
[tex]1. 25x^4 - 10x^3 + x^2[/tex]
[tex]2. 5x^4 - x^3[/tex]
[tex]3. x^4[/tex]
Let's factorize each polynomial:
1.[tex]25x^4 - 10x^3 + x^2[/tex] can be factored as[tex](5x^2 - x)(5x^2 - x).[/tex]
2.[tex]5x^4 - x^3[/tex] is already in its simplest form and cannot be factored further.
3.[tex]x^4[/tex] is also in its simplest form and cannot be factored further.
Now, we need to find the LCM of these factorized polynomials. The LCM is the product of the highest power of each unique factor.
Looking at the factorized forms, we can see that the highest power of [tex](5x^2 - x)[/tex] is 1 and the highest power of x is 4. Therefore, the LCM will be[tex](5x^2 - x)(x^4).[/tex]
Thus, the LCM of the given polynomials is [tex](5x^2 - x)(x^4).[/tex]
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