The middle term in the polynomial $2{x^2} - 5x + 3$ is $- 5x$ . This must be expressed as a sum of two terms such that the product of their coefficients is equal to the product of 2 and 3 (coefficient of x² and the constant term)

−5 can be expressed as $( - 2) + ( - 3)$ , as $- 2 \times - 3 = 6 = 2 \times 3$

Thus, $2{x^2} - 5x + 3 = 2{x^2} - 2x - 3x + 3$

Now, identify the common factors in individual groups

$2{x^2} - 2x - 3x + 3 = 2x(x - 1) - 3(x - 1)$

Taking (x−1) as the common factor, this can be expressed as:

$2x(x - 1) - 3(x - 1) = (x - 1)(2x - 3)$

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