Question

Factor completely:
2t²+5t-3 Please explain how you did it! Thanks!

Answer 1

(2t -1 )( t+3 )

Answer 2

2t^2 + 2t + 3t - 3
2t(t + 1) + -3(t+1)
(2t -1)( t+3 )

Answer 3

how did you get that? I need to show work

Answer 4

Never mind

Answer 5

u sure?

Answer 6

Actually no I'm not. Could you explain how you got that?

Answer 7

sorry to be so long - i had to do a chore ok
this is the way i do them
what we need is two numbers which multiplied together with 2 = -6 and when added give + 5

make 3 columns and try out the combinations

2 -3 +5 aiming for +5
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2 x 1 3 x -1 2 x -1 + 1x3 = =1
2 x 1 3 x -1 3 x 2 + 1 x-1 = 6-1 = 5
- that is 3 with 2 and 1 with -1

so we get
(2t - 1)(t + 3)
outside 2t and 3 and inside -1 and 1t

Answer 8

so there can be three numbers?

Answer 9

I got confused after you put that the 2t is outside when its put inside,

Answer 10

in this case there are 3 numbers involved the 2 from 2t^2, the -3 and the 5 from 5t.
things are easier if the expression starts with x^2 then you only need two columns

Answer 11

yeah I know about that! I actually get those ones!

Answer 12

The ones with only x^2

Answer 13

what i meant was the +5t is formed from the two 'outside' numbers 2t and +3 and the 'inside' ones -1 and t

Answer 14

Alright, I kind of get it, the only thing is I have to show my work and I have no idea how to show this!

Answer 15

well - just write the 3 columns on right side of your page
- its a valid method and the one most favoured in the uk. i used to teach maths and i found most pupils understood this one best.

Answer 16

Ok

Answer 17

i find its better as you are writing down rather trying to figure out in your head
- its not the only way to proceed of course - in end its a matter of choice, what you find easiest

Answer 18

Yeah I definitely can't do stuff in my head by sides simple multiplication, adding subtracting, and dividing! Thanks so much for explaining!

Answer 19

ok - practice them and you'll find you'll get good at it