Factor the following trinomial: t^2 + 4t -2Show all work

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lfryerda | High School Teacher | (Level 2) Educator

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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-2`

`=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)` .