can anyone factorise 2x(squared) + 5x - 3?

2x^2 + 5x - 3
= 2x^2 + 6x - x - 3
= (2x^2 + 6x) - (x + 3)
= 2x(x + 3) - 1(x + 3)
= (x + 3)(2x - 1)

2x^2 + 5x - 3
For the 2x^2, you will have 2x in one part and x in the other
(2x + ??)(x + ??)
You then need to look at something that multiplies out to -3
That would be -3,1 or 3,-1
The other part is the 2 numbers need add to 5 and one will be multiplied by 2.
If the 3 or -3 is in the 1st parenthesis, then it will add up to 1x or -1x.
If you put it into the 2nd parenthesis, then you have 3*2 for 6, and if you subtract 1 you get your five.
(2x - 1)(x + 3) = 2x^2 + 6x - 1x -3 = 2x^2 + 5x - 3

2x 2 5x 3

( 2x - 1 ) ( x + 3 )

yes.

Oh you want more than that? ;-)

ok... the 2x² must factorise into (2x....)(x....) and the -3 must factorise into a 3 and a 1 (and one of them must have a minus sign to give -3) so all that is left is to work out which way the around the 3 and 1 go into the brackets.
(2x+1)(x-3) = 2x²-5x-3 so that doesn't work
(2x+3)(x-1) = 2x²+x-3 so that doesn't work
(2x-3)(x+1) = 2x²-x-3 so that doesn't work
(2x-1)(x+3) = 2x²+5x-3

( 2x - 1 ) ( x + 3 )

2x^2 + 5x -3 = (x + 3 ) (2x - 1)

( 2x - 1 ) ( x + 3 )

2x^2+5x-3


a=2 b=5 c=-3

-5+/- sqrt 5^2-4(2)(-3)/4

-5+/-sqrt 25+24/4
-5 +/- sqrt 49/4
-5+/-7/4
x=2/4=1/2 or -12/4=-3
x=1/2 or -3

x= -5 (+-) square root( 25 +24) / 4

X= -5 +- 7 / 4

x= 1/2
x = -3

2x^2 + 5x -3 = (x+3)(x-1/2)