Factor : (4x^2-7x+3) - (3x^2-5x)

(4x^2-7x+3) - (3x^2-5x)

= (x-1)(4x-3)-x(3x+5)
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My guess as to what the problem is needing:

(4x^2 - 7x + 3) - (3x^2 - 5x)

remove parentheses then combine like terms

4x^2 - 7x + 3 - 3x^2 + 5x
4x^2 - 3x^2 - 7x + 5x + 3
x^2 - 2x + 3

Then factor x^2 - 2x + 3

To factor the expression (4x^2 - 7x + 3) - (3x^2 - 5x), we will first distribute the negative sign to the terms inside the parentheses.

(4x^2 - 7x + 3) - (3x^2 - 5x) becomes:

4x^2 - 7x + 3 - 3x^2 + 5x

Next, we combine the like terms:

(4x^2 - 3x^2) + (-7x + 5x) + 3

Simplifying further:

x^2 - 2x + 3

We cannot factor this quadratic expression any further using integers or rational numbers. Therefore, the factored form of the expression (4x^2 - 7x + 3) - (3x^2 - 5x) is x^2 - 2x + 3.