1)) Simplify.Write your answer using whole numbers and variables. (2x^2-10x+12)/(x-3) square

To simplify the expression \(\frac{2x^2 - 10x + 12}{x - 3}\), we need to factor the numerator and see if it has a common factor with the denominator.<br /><br />First, let's factor the numerator \(2x^2 - 10x + 12\):<br /><br />1. Factor out the greatest common factor (GCF) from the numerator:<br /> \[<br /> 2x^2 - 10x + 12 = 2(x^2 - 5x + 6)<br /> \]<br /><br />2. Now, factor the quadratic expression \(x^2 - 5x + 6\):<br /> \[<br /> x^2 - 5x + 6 = (x - 2)(x - 3)<br /> \]<br /><br />So, the numerator becomes:<br />\[<br />2(x - 2)(x - 3)<br />\]<br /><br />Now, rewrite the original expression with the factored form of the numerator:<br />\[<br />\frac{2(x - 2)(x - 3)}{x - 3}<br />\]<br /><br />3. Cancel the common factor \((x - 3)\) in the numerator and the denominator:<br />\[<br />\frac{2(x - 2)\cancel{(x - 3)}}{\cancel{x - 3}} = 2(x - 2)<br />\]<br /><br />Thus, the simplified form of the given expression is:<br />\[<br />\boxed{2(x - 2)}<br />\]