Đáp án:
$\displaystyle \begin{array}{{>{\displaystyle}l}} a.( x-5)( x+1)\\ b.( 2x+1)( x-1)\\ c.( 3x-2)( x+1)\\ d.( x+3)( x-7)\\ e.\left( x-\frac{1}{4}\right)( x+2)\\ g.( x+y)( x-5y)\\ h.( 2x+y)( x-y)\\ i.( 3x-2y)( x+y)\\ k.( x+3y)( x-7y)\\ l.\left( x-\frac{1}{4} y\right)( x+2y) \ \end{array}$
Giải thích các bước giải:
$\displaystyle \begin{array}{{>{\displaystyle}l}} a.\ M=x^{2} -4x-5=x^{2} +x-5x-5\\ =x( x+1) -5( x+1) =( x-5)( x+1)\\ b.\ N=2x^{2} -x-1=2x^{2} -2x+x-1\\ =2x( x-1) +( x-1) =( 2x+1)( x-1)\\ c.\ P=3x^{2} +x-2=3x^{2} +3x-2x-2\\ =3x( x+1) -2( x+1) =( 3x-2)( x+1)\\ d.\ Q=x^{2} -4x-21=x^{2} -7x+3x-21\\ =x( x-7) +3( x-7) =( x+3)( x-7)\\ e.\ E=x^{2} +\frac{7}{4} x-\frac{1}{2} =x^{2} +2x-\frac{1}{4} x-\frac{1}{2}\\ =x( x+2) -\frac{1}{4}( x+2) =\left( x-\frac{1}{4}\right)( x+2)\\ g.\ G=x^{2} -4xy-5y^{2} =x^{2} -5xy+xy-5y^{2}\\ =x( x-5y) +y( x-5y) =( x+y)( x-5y)\\ h.\ H=2x^{2} -xy-y^{2} =2x^{2} -2xy+xy-y^{2}\\ =2x( x-y) +y( x-y) =( 2x+y)( x-y)\\ i.\ I=3x^{2} +xy-2y^{2} =3x^{2} +3xy-2xy-2y^{2}\\ =3x( x+y) -2y( x+y) =( 3x-2y)( x+y))\\ k.\ K=x^{2} -4xy-21y^{2} =x^{2} -7xy+3xy-21y^{2}\\ =x( x-7y) +3y( x-7y) =( x+3y)( x-7y)\\ l.\ L=x^{2} +\frac{7}{4} xy-\frac{1}{2} y^{2} =x^{2} +2xy-\frac{1}{4} xy-\frac{1}{2} y^{2}\\ =x( x+2y) -\frac{1}{4} y( x+2y) =\left( x-\frac{1}{4} y\right)( x+2y) \end{array}$
