Step 1: We rewrite the middle terms as a sum of two terms whose product is a·c = 2·6 = 12 and whose sum is b = -7.
[tex]2x^2-7x+6=2x^2-3x-4x+6[/tex]Step 2 We group the first two terms and last two terms.
[tex]2x^2-7x+6=(2x^2-3x)-4x+6[/tex]Step 3: We factor out the greatest common factor from each group.
[tex]2x^2-7x+6=x(2x-3)-2(2x-3)[/tex]Step 4: We factor the polynomial by factoring out the greatest common factor, 2x - 3.
[tex]2x^2-7x+6=(2x-3)(x-2)[/tex]We cancel the common factor.
[tex]\begin{gathered} \frac{2x^2-7x+6}{x-2}=\frac{(2x-3)(x-2)}{x-2} \\ \frac{2x^2-7x+6}{x-2}=2x-3 \end{gathered}[/tex]Answer[tex]2x-3[/tex]