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Đáp án:
`2)`
$x^2+2x-3$
$=x^2+3x-x-3$
$=x.(x+3)-1.(x+3)$
$=(x+3).(x-1)$
`3)`
$x^2-10x+9$
$=x^2-x-9x+9$
$=x.(x-1)-9.(x-1)$
$=(x-9).(x-1)$
`4)`
$x^2-2x-15$
$= x^2+3x-5x-15$
$=x.(x+3)-5.(x+3)$
$=(x-5).(x+3)$
`5)`
$x^2-2x-48$
$=x^2+6x-8x-48$
$=x.(x+6)-8.(x+6)$
$= (x-8).(x+6)$
`6)`
$x^2-10x+24$
$= x^2-4x-6x+24$
$= x.(x-4)-6.(x-4)$
$=(x-6).(x-4)$
`7)`
$4x^2+4x-15$
$= 4x^2+10x-6x-15$
$=2x.(2x+5)-3.(2x+5)$
$=(2x+5).(2x-3)$
`8)`
$3x^2-7x+2$
$=3x^2-x-6x+2$
$= x.(3x-1)-2.(3x-1)$
$=(3x-1).(x-2)$
`9)`
$4x^2-5x+1$
$= 4x^2-x-4x+1$
$= x.(4x-1)-1.(4x-1)$
$=(x-1).(4x-1)$
`10)`
$x^2-25x+24$
$= x^2-x-24x+24$
$=x.(x-1)-24.(x-1)$
$=(x-24).(x-1)$
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Giải thích các bước giải:
`2.`
`x^2 + 2x - 3`
`= x^2 - x + 3x - 3`
`= x(x - 1) + 3(x - 1)`
`= (x + 3)(x - 1)`
`-------------`
`3.`
`x^2 - 10x + 9`
`= x^2 - x - 9x + 9`
`= x(x - 1) - 9(x - 1)`
`= (x - 9)(x - 1)`
`-------------`
`4.`
`x^2 - 2x - 15`
`= x^2 + 3x - 5x - 15`
`= x(x + 3) - 5(x + 3)`
`= (x - 5)(x + 3)`
`-----------------`
`5.`
`x^2 - 2x - 48`
`= x^2 - 8x + 6x - 48`
`= x(x - 8) + 6(x - 8)`
`= (x + 6)(x - 8)`
`----------------`
`6)` `x^2-10x+24` `=x^2-2.x.5+5^2-1`
`=(x-5)^2-1>=-1AAx`
Dấu "`=`" xảy ra
`<=>x-5=0<=>x=5`
Vậy Min `x^2-10x+24=-1<=>x=5`
`-------------------`
`7.`
`4x^2+4x-15`
`=(2x)^2+2.2x.1+1^2-16`
`=(2x+1)^2-16>=-16AAx`
Dấu "`=`" xảy ra
`<=>2x+1=0<=>2x=-1<=>x=-1/2`
Vậy Min `4x^2+4x-15=-16<=>x=-1/2`
`-------------`
`8.` `3x^2-7x+2` `=3(x^2-7/3x+2/3)`
`=3[x^2-2.x. 7/6+(7/6)^2-25/36]`
`=3[(x-7/6)^2-25/36]`
`=3(x-7/6)^2-25/12>=-25/12AAx`
Dấu "`=`" xảy ra
`<=>x-7/6=0<=>x=7/6`
Vậy Min `3x^2-7x+2=-25/12<=>x=7/6`
`-----------------`
`9`.
`4x^2-5x+1`
`=(2x)^2-2.2x. 5/4+(5/4)^2-9/16`
`=(2x-5/4)^2-9/16>=-9/16AAx`
Dấu "`=`" xảy ra
`<=>2x-5/4=0<=>2x=5/4<=>x=5/4:2<=>x=5/8`
Vậy Min `4x^2-5x+1=-9/16<=>x=5/8`
`---------`
`10.`
`x^2-25x+24`
`=x^2-2.x. 25/2+(25/2)^2-529/4`
`=(x-25/2)^2-529/4>=-529/4AAx`
Dấu "`=`" xảy ra
`<=>x-25/2=0<=>x=25/2`
Vậy Min `x^2-25x+24=-529/4<=>x=25/2`
`----------------`
`#Michan`
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