Find the factors of the algebraic expression \(2x^2 - 5x - 3\).

Step 1 ：Step 1: Write the expression in standard form, which is \(ax^2 + bx + c\). Here, \(a = 2\), \(b = -5\), and \(c = -3\).

Step 2 ：Step 2: Multiply \(a\) and \(c\), which gives \(2*(-3) = -6\).

Step 3 ：Step 3: Find two numbers that multiply to \(-6\) and add to \(-5\). The numbers are \(-6\) and \(1\).

Step 4 ：Step 4: Rewrite the middle term of the expression as the sum of the terms \(-6x\) and \(x\). This gives \(2x^2 - 6x + x - 3\).

Step 5 ：Step 5: Group the terms to get \((2x^2 - 6x) + (x - 3)\).

Step 6 ：Step 6: Factor by grouping. This gives \(2x(x - 3) + 1(x - 3)\).

Step 7 ：Step 7: Notice that \((x - 3)\) is a common factor. We can then write the expression as \((2x + 1)(x - 3)\).