6 One factor of 2a2 53 is A 3 Ba 1 C z1 D 2r 1 E 2r 3 Soluti

6. One factor of 2a2 53 is (A) -3 (B)a 1 (C) z+1 (D) 2r +1 (E) 2r +3

2x^2 - 5x + 3

This is a quadratic that can clearly be factored...
So, lets do it...

2x^2 - 5x + 3

Standard quad is ax^ 2+ bx + c

So, by comparing, we get :
a = 2 , b = -5 and c = 3

And rules for factoring a QUADRATIC is :
Sum of two numbers = b
Product of two numbers = ac

So, here we have :
Sum = -5
Product = 2*3 = 6

Now, which two numbers add up to -5 and also multiply to yield 6?
Oh yeah, tis -2 and -3

So, we now have :
2x^2 - 5x + 3 as

2x^2 - 2x - 3x + 3

Now, pair first two terms and last two terms and then factor :
2x(x - 1) - 3(x - 1)

Now, take that x - 1 out in common to get :
(2x - 3)(x - 1)
as the final factored form

So, one of the factors was :
x - 1

Option B is the answer