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Answer :
Let's factorize the given expressions step-by-step.
Factorizing the expression 19x^5 - 38x^3:
We start by identifying the greatest common factor (GCF) of the terms. Here, the GCF is 19x^3.
Let's factor out the GCF:
[tex]19x^5 - 38x^3 = 19x^3(x^2 - 2).[/tex]
Therefore, the factorized form is [tex]19x^3(x^2 - 2)[/tex].
Factorizing the expression (x-1)^2 - 3(x-1):
Notice that [tex](x - 1)[/tex] is a common factor in both terms.
Let's factor [tex](x - 1)[/tex] out:
[tex](x-1)^2 - 3(x-1) = (x-1)((x-1) - 3).[/tex]
Simplify inside the parentheses:
[tex](x-1)((x-1) - 3) = (x-1)(x-1 - 3)
= (x-1)(x-4).[/tex]Therefore, the factorized form is [tex](x-1)(x-4)[/tex].
Factorizing the expression 3:
The number 3 is a constant and cannot be factorized further with variables or other expressions.
The factorized form of a constant like 3 remains the same: [tex]3[/tex].
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