Question

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Answer 1

Factorization of the given polynomial to find the product is as follows;

Factorizing;

$\dfrac{x^2 + 3*x +2}{x^2+ 6*x + 5} = \dfrac{(x + 1) * (x + 2)}{(x + 1)*(x + 5)}$

$\dfrac{x^2 + 7*x +10}{x^2+ 4*x + 4} = \dfrac{(x + 2) * (x + 5)}{(x + 2)*(x + 2)}$

Expressing the product in terms of the factors

$\dfrac{x^2 + 3*x +2}{x^2+ 6*x + 5} \times \dfrac{x^2 + 7*x +10}{x^2+ 4*x + 4} = \dfrac{(x + 2) * (x + 5)}{(x + 2)*(x + 2)} \times \dfrac{(x + 1) * (x + 2)}{(x + 1)*(x + 5)}$

The steps arranged in the order in which they would be performed are;

First step;

$\dfrac{x^2 + 3*x +2}{x^2+ 6*x + 5} \times \dfrac{x^2 + 7*x +10}{x^2+ 4*x + 4}$

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Second step (factorizing)

$\dfrac{(x + 2) * (x + 5)}{(x + 2)*(x + 2)} \times \dfrac{(x + 1) * (x + 2)}{(x + 1)*(x + 5)}$

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Third step (dividing out common terms)

$\dfrac{(x + 5)}{(x + 2)} \times \dfrac{(x + 2)}{(x + 5)}$

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Fourth step (rearranging and removing terms that cancel each other)

1

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brainly.com/question/12723898