Đáp án:
$1) 2(x+3)(x-1)\\
2)
(x+3)(3x-2)\\
3)
(x-4)(3x+2)\\
4)
(x-4+\sqrt{6})(x-4-\sqrt{6})\\
5)
2(x+5+\sqrt{21})(x+5-\sqrt{21})\\
6)
(x-1)(6x^2+6x-1)\\$
Giải thích các bước giải:
$1) 2x^2+4x-6\\
=2(x^2+2x-3)\\
=2(x^2+3x-x-3)\\
=2\left [ x(x+3)-(x+3) \right ]
=2(x+3)(x-1)\\
2)
3x^2+7x-6\\
=3x^2-2x+9x-6\\
=x(3x-2)+3(3x-2)\\
=(x+3)(3x-2)\\
3)
3x^2-10x-8\\
=3x^2+2x-12x-8\\
=x(3x+2)-4(3x+2)\\
=(x-4)(3x+2)\\
4)
x^2-8x+10\\
=x^2-4x+\sqrt{6}x-4x+16-4\sqrt{6}-\sqrt{6}x+4\sqrt{6}-6\\
=\left [x^2-(4-\sqrt{6})x \right ]-(4x-16+4\sqrt{6})-(\sqrt{6}x-4\sqrt{6}+6)\\
=x(x-4+\sqrt{6})-4(x-4+\sqrt{6})-\sqrt{6}(x-4+\sqrt{6})\\
=(x-4+\sqrt{6})(x-4-\sqrt{6})\\
5)
2x^2+20x+8\\
=2(x^2+10x+4)\\
=2\left (x^2+5x+\sqrt{21}x+5x+25+5\sqrt{21}-\sqrt{21}x-5\sqrt{21}-21 \right )\\
=2\left [ x(x+5+\sqrt{21})+5(x+5+\sqrt{21})-\sqrt{21}(x+5+\sqrt{21}) \right ]\\
=2(x+5+\sqrt{21})(x+5-\sqrt{21})\\
6)
6x^3-7x+1\\
=6x^3+6x^2-x-6x^2-6x+1\\
=x(6x^2+6x-1)-(6x^2+6x-1)\\
=(x-1)(6x^2+6x-1)\\$
