Can someone please factor this

2x^2+5x-3.

Show work.

2x^2+5x-3
(2x -1)(x + 3) Check it!
2x^2 +6x -x -3
2x^2 + 5x - 3

Two ways:

first look at the quadratic solution:
x = (-5 +/-sqrt(25 +24))/4
==> x = -12/4 or x= 2/4
==> x = -3 or x= 1/2
So, (x + 3)(2x - 1)

or
You know that if there are factors, they take the form (ax + b)(cx +d)
multiplied out, this gives acx^2 +(ad + bc)x + bd
ac = 2
(ad + bc) = 5
bd = -3
Solving this:
we eventually get to a = 2, b = -1, c = 1 and d = 3
so: (2x -1)(x+ 3)

Begin with quadratic formula.

x = -b ± √(b^2 - 4ac)/2a

Plug in values of a, b, and c.

a = 2, b = 5, c = -3

x = -(5) ± √((5)^2 - 4(2)(-3))/2(2)

Simplify

x = (-5 ± √(25 - (-24)))/4
x = (-5 ± √(49))/4
x = (-5 ± 7)/4

This gives us two possibilities.

x = (-5 + 7)/4
x = (-5 - 7)/4

x = 2/4
x = -12/4

x = 1/2
x = -3

Now, we know what x is, but that is not what the question asked us. We still need to factor it. Watch this.

x - 1/2 = 0
x + 3 = 0

(x - 1/2)(x + 3) = 0

(x - 1/2)(x + 3) is the answer. However, this can be also written as (2x - 1)(x + 3) = 0

Hope this helps.

( 2x - 1 ) ( x + 3 )

(2x - 1)(x + 3)