Write polynomial $P$ as a product of linear factors: $P (x) = (x + 2) (20 x^{2} + 41 x + 20)$

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Solution

We know that $P (x) = (x + 2) (20 x^{2} + 41 x + 20)$
Solving the term $(20 x^{2} + 41 x + 20)$
Seperating the terms in such a way that the product is $400$ that is $(20 \times 20)$ and sum is $41$
$= 20 x^{2} + 16 x + 25 x + 20$
Taking the common terms
$= 5 x (4 x + 5) + 4 (4 x + 5)$
$= (5 x + 4) (4 x + 5)$
The ans is $(x + 2) (5 x + 4) (4 x + 5)$

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