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t^2 + 4t -2
= t^2 +2x2t + 2^2 - 6
= (t+2)^2 - 6
= (t+2)^2 - (√6)^2
= (t+2+ √6) x (t+2 -√6)
If you look at the discriminant of the trinomial `t^2+4t-2` , we get `D=4^2-4(-2)=16+8=24` , which is not a perfect square. This means that we need to use completing the square to properly factor.
`=t^2+4t+4-4-2` add and subtract a number to make first 3 terms a perfect square
`=(t+2)^2-6` now treat as a difference of squares
`=(t+2-sqrt 6)(t+2+sqrt 6)`
The trinomial factors into `(t+2-sqrt 6)(t+2+sqrt 6)` .
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