Question

Medal and Fan for helping me solve this.

Answer 1

@Michele_Laino

Answer 2

first step:
we can factor out \(2\), so we can write this:
\[2\left( {{x^2} + 5x + 6} \right)\]
now, we have to factor the trinomial:
\[ {{x^2} + 5x + 6} \]
in order to do that, please try to find two number such that their sum is \(-5\) and theyr product is \(6\)

Answer 3

numbers*

Answer 4

Factors of -5 and 6?

Answer 5

for example you can find such numbers, among the divisors of \(6\):
\(\pm 2, \;\pm 3,\;\pm6,\;\pm1\)

Answer 6

-3 and -2

Answer 7

that's right!
so the requested factorization is:
\[\Large \begin{gathered}
2\left( {{x^2} + 5x + 6} \right) = 2\left( {x - \left( { - 2} \right)} \right)\left( {x - \left( { - 3} \right)} \right) = \hfill \\
\hfill \\
= 2\left( {x + 2} \right)\left( {x + 3} \right) \hfill \\
\end{gathered} \]

Answer 8

Got it

Answer 9

:)

Answer 10

:)