Splitting the middle term:

Splitting the middle term:

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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