Đáp án:

$1)\left(x-3\right)\left(x-2\right)\\ 2)\left(x+2\right)\left(x+3\right)\\ 3)\left(x-4\right)\left(x-3\right)\\ 4)\left(x+3\right)\left(x+4\right)\\ 5)\left(x-3\right)\left(x+4\right)\\ 6)\left(x-4\right)\left(x+3\right)\\ 7)\left(x-5\right)\left(x-4\right)\\ 8)\left(x+4\right)\left(x+5\right)\\ 9)\left(x-4\right)\left(x+5\right)\\ 10)\left(x-5\right)\left(x+4\right)$

Giải thích các bước giải:

$1)x^2-5x+6\\ =x^2-2.x.\dfrac{5}{2}+\dfrac{25}{4}-\dfrac{1}{4}\\ =\left(x-\dfrac{5}{2}\right)^2-\left(\dfrac{1}{2}\right)^2\\ =\left(x-\dfrac{5}{2}-\dfrac{1}{2}\right)\left(x-\dfrac{5}{2}+\dfrac{1}{2}\right)\\ =\left(x-3\right)\left(x-2\right)\\ 2)x^2+5x+6\\ =x^2+2.x.\dfrac{5}{2}+\dfrac{25}{4}-\dfrac{1}{4}\\ =\left(x+\dfrac{5}{2}\right)^2-\left(\dfrac{1}{2}\right)^2\\ =\left(x+\dfrac{5}{2}-\dfrac{1}{2}\right)\left(x+\dfrac{5}{2}+\dfrac{1}{2}\right)\\ =\left(x+2\right)\left(x+3\right)\\ 3)x^2-7x+12\\ =x^2-2.x.\dfrac{7}{2}+\dfrac{49}{4}-\dfrac{1}{4}\\ =\left(x-\dfrac{7}{2}\right)^2-\left(\dfrac{1}{2}\right)^2\\ =\left(x-\dfrac{7}{2}-\dfrac{1}{2}\right)\left(x-\dfrac{7}{2}+\dfrac{1}{2}\right)\\ =\left(x-4\right)\left(x-3\right)\\ 4)x^2+7x+12\\ =x^2+2.x.\dfrac{7}{2}+\dfrac{49}{4}-\dfrac{1}{4}\\ =\left(x+\dfrac{7}{2}\right)^2-\left(\dfrac{1}{2}\right)^2\\ =\left(x+\dfrac{7}{2}-\dfrac{1}{2}\right)\left(x+\dfrac{7}{2}+\dfrac{1}{2}\right)\\ =\left(x+3\right)\left(x+4\right)\\ 5)x^2+x-12\\ =x^2+2.x.\dfrac{1}{2}+\dfrac{1}{4}-\dfrac{49}{4}\\ =\left(x+\dfrac{1}{2}\right)^2-\left(\dfrac{7}{2}\right)^2\\ =\left(x+\dfrac{1}{2}-\dfrac{7}{2}\right)\left(x+\dfrac{1}{2}+\dfrac{7}{2}\right)\\ =\left(x-3\right)\left(x+4\right)\\ 6)x^2-x-12\\ =x^2-2.x.\dfrac{1}{2}+\dfrac{1}{4}-\dfrac{49}{4}\\ =\left(x-\dfrac{1}{2}\right)^2-\left(\dfrac{7}{2}\right)^2\\ =\left(x-\dfrac{1}{2}-\dfrac{7}{2}\right)\left(x-\dfrac{1}{2}+\dfrac{7}{2}\right)\\ =\left(x-4\right)\left(x+3\right)\\ 7)x^2-9x+20\\ =x^2-2.x.\dfrac{9}{2}+\dfrac{81}{4}-\dfrac{1}{4}\\ =\left(x-\dfrac{9}{2}\right)^2-\left(\dfrac{1}{2}\right)^2\\ =\left(x-\dfrac{9}{2}-\dfrac{1}{2}\right)\left(x-\dfrac{9}{2}+\dfrac{1}{2}\right)\\ =\left(x-5\right)\left(x-4\right)\\ 8)x^2+9x+20\\ =x^2+2.x.\dfrac{9}{2}+\dfrac{81}{4}-\dfrac{1}{4}\\ =\left(x+\dfrac{9}{2}\right)^2-\left(\dfrac{1}{2}\right)^2\\ =\left(x+\dfrac{9}{2}-\dfrac{1}{2}\right)\left(x+\dfrac{9}{2}+\dfrac{1}{2}\right)\\ =\left(x+4\right)\left(x+5\right)\\ 9)x^2+x-20\\ =x^2+2.x.\dfrac{1}{2}+\dfrac{1}{4}-\dfrac{81}{4}\\ =\left(x+\dfrac{1}{2}\right)^2-\left(\dfrac{9}{2}\right)^2\\ =\left(x+\dfrac{1}{2}-\dfrac{9}{2}\right)\left(x+\dfrac{1}{2}+\dfrac{9}{2}\right)\\ =\left(x-4\right)\left(x+5\right)\\ 10)x^2-x-20\\ =x^2-2.x.\dfrac{1}{2}+\dfrac{1}{4}-\dfrac{81}{4}\\ =\left(x-\dfrac{1}{2}\right)^2-\left(\dfrac{9}{2}\right)^2\\ =\left(x-\dfrac{1}{2}-\dfrac{9}{2}\right)\left(x-\dfrac{1}{2}+\dfrac{9}{2}\right)\\ =\left(x-5\right)\left(x+4\right)$