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

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### 2 Answers

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)` .**

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)