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

2 Answers | Add Yours

lfryerda's profile pic

lfryerda | High School Teacher | (Level 2) Educator

Posted on

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)` .

anhmaitran93's profile pic

anhmaitran93 | Student, College Freshman | eNotes Newbie

Posted on

   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)

We’ve answered 318,974 questions. We can answer yours, too.

Ask a question