Factorize the trinomial \(2x^2 - 5x - 3\)

Step 1 ：In order to factorize the trinomial, we need to find two numbers that multiply to \(2*(-3) = -6\) and add up to \(-5\)

Step 2 ：The numbers that satisfy this condition are \(-6\) and \(1\), because \(-6 + 1 = -5\) and \(-6 * 1 = -6\)

Step 3 ：We rewrite the middle term of the trinomial using these two numbers: \(2x^2 - 6x + x - 3\)

Step 4 ：Then we factor by grouping: \(2x(x - 3) + 1(x - 3)\)

Step 5 ：Finally, we factor out the common binomial factor to get the final factorized form: \((2x + 1)(x - 3)\)