Factorise 2t^2+5t+2 and pls explain why 2t(t+2) becomes (2t+1) when you get to it in your working out ty

Question

Factorise
`2t^2+5t+2`

and pls explain why 2t(t+2) becomes (2t+1) when you get to it in your working out ty

Answer 1

Answer:
`\displaystyle\ \large \boldsymbol{ 2t^2+5t+2= {(2t+1) (t+2)}}`

Explanation:

`\displaystyle\ \large \boldsymbol{} 2t^2+5t+2=0 \\\\2t^2+\underbrace{4t+t}_(5t)+2=0 \\\\ (2t^2+4t)+(t+2)=0 \\\\ 2t(\underline{t+2})+(\underline{t+2})=0 \\\\ \boxed{(2t+1) (t+2)=0 }`