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=6x^2 - 4x - 9x +6
=(6x^2 -4x) - (9x-6)
=2x(3x -2) - 3(3x-2)
=(3x-2) (2x - 3)
\(6x^2+13x-15\)
\(=6x^2+18x-5x-15\)
\(=6x.\left(x+3\right)-5.\left(x+3\right)\)
\(=\left(x+3\right).\left(6x-5\right)\)
\(6x^2+13x-15\)
\(=6x^2+18x-5x-15\)
\(=6x\left(x+3\right)-5\left(x+3\right)\)
\(=\left(x+3\right)\left(6x-5\right)\)
\(P\left(x\right)=6x^3+13x^2+4x-3\)
\(=\left(6x^3+6x^2\right)+\left(7x^2+7x\right)-\left(3x-3\right)\)
\(=6x^2\left(x+1\right)+7x\left(x+1\right)-3\left(x+1\right)\)
\(=\left(6x^2+7x-3\right)\left(x+1\right)\)
\(=\left[\left(6x^2-2x\right)+\left(9x-3\right)\right]\left(x+1\right)\)
\(=\left[2x\left(3x-1\right)+3\left(3x-1\right)\right]\left(x+1\right)\)
\(=\left(3x-1\right)\left(2x+3\right)\left(x+1\right)\)
1) 6x^2 + 7x - 5
=6x2-3x+10x-5
=3x.(2x-1)+5.(2x-1)
=(2x-1)(3x+5)
2) 10x^2 - 13x - 3
=10x2+2x-15x-3
=2x(5x+1)-3(5x+1)
=(5x+1)(2x-3)
\(6x^2+7x-5\)
\(=6x^2-3x+10x-5\)
\(=3x\left(2x-1\right)+5\left(2x-1\right)\)
\(=\left(2x-1\right)\left(3x+5\right)\)
Bài làm:
a) \(x^2-6x+4=\left(x^2-6x+9\right)-5=\left(x-3\right)^2-\left(\sqrt{5}\right)^2\)
\(=\left(x-3-\sqrt{5}\right)\left(x-3+\sqrt{5}\right)\)
b) \(x^2-4x+3=x^2-x-3x+3=\left(x-1\right)\left(x-3\right)\)
c) \(6x^2-5x+1=6x^2-3x-2x+1=\left(2x-1\right)\left(3x-1\right)\)
d) \(3x^2+13x-10=3x^2+15x-2x-10=\left(x-5\right)\left(3x-2\right)\)
Ta có (6x+5)2(3x+2)(x+1)-35
= (36x2+60x+25)(3x2+5x+2)-35 (1)
Đặt a=3x2+5x+2
=> 12a+1= 12(3x2+5x+2)+1 =36x2+60x+25
Thay a=3x2+5x+2 vào (1) ta được
(12a+1).a-35=12a2+a-35
= 12a2-20a+21a-35
= 4a(3a-5)+7(3a-5)
= (3a-5)(4a+7) (2)
Thay 3x2+5x+2=a vào (2) ta được
(9x2+15x+6-5)(12x2+20x+8+7)
= (9x2+15x+1)(12x2+20x+15)
Ta có: \(\left(6x+5\right)^2\left(3x+2\right)\left(x+1\right)-35\)
\(=\left(36x^2+60x+25\right)\left(3x^2+5x+2\right)-35\)(1)
Đặt \(3x^2+5x+2=y\)
\(\left(1\right)=\left(12y+1\right)y-35\)
\(=12y^2+y-35\)
\(=\left(3y-5\right)\left(4y+7\right)\)
\(=\left(9x^2+15x+1\right)\left(12x^2+20x+15\right)\)
\(b,x^2+6x+5=x^2+x+5x+5=x\left(x+1\right)+5\left(x+1\right)=\left(x+1\right)\left(x+5\right)\)
\(c,x^2-7x+10=x^2-2x-5x+10=x\left(x-2\right)-5\left(x-2\right)=\left(x-2\right)\left(x-5\right)\)
\(=6x^2+3x+10x+5=3x\left(2x+1\right)+5\left(2x+1\right)=\left(3x+5\right)\left(2x+1\right)\)
6x2+3x+10x+5=3x(2x+1)+5(2x+1)=(3x+5)(2x+1)