Factorization of the given polynomial to find the product is as follows;
Factorizing;
[tex]\dfrac{x^2 + 3*x +2}{x^2+ 6*x + 5} = \dfrac{(x + 1) * (x + 2)}{(x + 1)*(x + 5)}[/tex]
[tex]\dfrac{x^2 + 7*x +10}{x^2+ 4*x + 4} = \dfrac{(x + 2) * (x + 5)}{(x + 2)*(x + 2)}[/tex]
Expressing the product in terms of the factors
[tex]\dfrac{x^2 + 3*x +2}{x^2+ 6*x + 5} \times \dfrac{x^2 + 7*x +10}{x^2+ 4*x + 4} = \dfrac{(x + 2) * (x + 5)}{(x + 2)*(x + 2)} \times \dfrac{(x + 1) * (x + 2)}{(x + 1)*(x + 5)}[/tex]
The steps arranged in the order in which they would be performed are;
First step;
[tex]\dfrac{x^2 + 3*x +2}{x^2+ 6*x + 5} \times \dfrac{x^2 + 7*x +10}{x^2+ 4*x + 4}[/tex]
↓
Second step (factorizing)
[tex]\dfrac{(x + 2) * (x + 5)}{(x + 2)*(x + 2)} \times \dfrac{(x + 1) * (x + 2)}{(x + 1)*(x + 5)}[/tex]
↓
Third step (dividing out common terms)
[tex]\dfrac{(x + 5)}{(x + 2)} \times \dfrac{(x + 2)}{(x + 5)}[/tex]
↓
Fourth step (rearranging and removing terms that cancel each other)
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