Question

How do I factor s^2+st-2t^2?

A lot of the time I just guess and check, but what's the logical way to factor this?

Answer 1

(s-t)(s+2t)

Answer 2

seems to work

Answer 3

it does. but how did you figure that out?

Answer 4

a regular trinomial you look to see what adds to the value of b and multiplies to c, what about here?

Answer 5

(-1)(2t + s)(t - s)

Answer 6

(2t^2 - s*t - t^2)

-s^2?

Answer 7

(-1)(2t^2 - s*t - s^2)

want -s^2 for the multiply part and -1s for the addition part
\[(-1)(2t \pm~~~)(t \pm~~~~)\]

Answer 8

why -1s?

Answer 9

that is the coefficient on the t term

Answer 10

so leave out the t?

Answer 11

i put the t's in the parenthesis already, you just have to fill in the plus or minus and the s's

Answer 12

(-1) (2t + s)(t - s)

u can see that the factors will be just 1s and 1s, then just test out where the + and - should go

Answer 13

+1s - 2s = -s

Answer 14

alright. i kind of get it now.

Answer 15

i'll try this the next time i get something like this

Answer 16

guess and check almost seems easier though, lol

Answer 17

it is just a game with the factors,
you can always use the quadratic formula and figure it out if needed

Answer 18

yeah guess and check is pretty much it, after you list the factors

Answer 19

got it. thanks

Answer 20

If you use the quadratic formula for

A=2
B= -s
C = -s^2

you will get those factors

Answer 21

let me try

Answer 22

-(2t^2 - s*t - s^2) = -(2t+s)(t-s)

t-s = 0 ... t = s
2t + s = 0 ....t = -1/2 s

quadratic formula will give the same

Answer 23

o.

Answer 24

\[\frac{ s \pm \sqrt{(-s)^2 - 4 * 2 * -s^2}}{ 4 } = \frac{ s \pm \sqrt{9s^2} }{ 4 } = \frac{ s \pm 3s }{ 4 }\]

Answer 25

4s/4 = s

-2s/4 = -1/2 s

Answer 26

which are the same values if you found the zeros to

-(2t+s)(t-s)

Answer 27

lol wow. didn't think of it like that.