how do you factor 2t^2 - 11t + 15?

Question

how do you factor 2t^2 - 11t + 15?
the 2t^2 means 2t squared
can you please explain it too?

Answer 1

You could use the quadatic equation, which is quite involved and I will not type.

This one is easy and I did it in my head...

(2t - 5) (t - 3)

Answer 2

quadratic equation is the best means.

but by inspection...

(at-b)(ct-d)=
(ac)t^2 +(-ad-cb)t +(bd)

ac=2
-ad-cb=-11
bd=15

Generally, it is whole number you will be factoring in these problems, so

a or c = 2 and 1
b or d = 3 and 5
how can you arrange those number such that
-ad-cb=-11 ?
-2(3)-1(5)=-11