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\(1,x^2+5x-6=x^2-x+6x-6=x\left(x-1\right)+6\left(x-1\right)=\left(x-1\right)\left(x+6\right)\)
\(3,7x-6x^2-2=-6x^2+7x-2=-6x^2+3x+4x-2=3x\left(-2x+1\right)+2\left(2x-1\right)\)
\(=3x\left(1-2x\right)-2\left(1-2x\right)=\left(1-2x\right)\left(3x-2\right)\)
\(2,5x^2+5xy-x-y=5x\left(x+y\right)-\left(x+y\right)=\left(x+y\right)\left(5x-1\right)\)
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a: =x^2+2x+3x+6
=(x+2)(x+3)
b: =5x(x+y)-(x+y)
=(x+y)(5x-1)
c: =-6x^2+3x+4x-2
=-3x(2x-1)+2(2x-1)
=(2x-1)(-3x+2)
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\(x^3-x^2-x+1\)
\(=x^2\left(x-1\right)-\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2-1\right)\)
Phân tích đa thức bằng cách phối hợp nhiều phương pháp
a,5xy3-2xyz-15y2+6z
b,x2(y-z)+y2(z-x)+z2(x-y)
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a, 5xy3-2xyz-15y2+6z
=5xy3-15y2+6z-2xyz
=5y2(xy-3)-2z(xy-3)
=(xy-3)(5y2-2z)
b, x2(y-z)+y2(z-x)+z2(x-y)
=x2y-x2z+y2z-y2x+z2(x-y)
=x2y-y2x-x2z+y2z+z2(x-y)
=xy(x-y)-z(x2-y2)+z2(x-y)
=xy(x-y)-z(x-y)(x+y)+z2(x-y)
=(x-y)[xy-z(x+y)+z2]
=(x-y)(xy-zx-zy+z2)
=(x-y)(xy-zx-zy+z2)
=(x-y)[x(y-z)-z(y-z)]
=(x-y)(y-z)(x-z)
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\(x^2+4x+3\)
\(=\left(x+1\right)\left(x+3\right)\)
\(2x^2+3x-5\)
\(\left(x-1\right)\left(x+\frac{5}{2}\right)\)
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\(3x^3+3x^2-36x\)
\(=3x\left(x^2+x-12\right)\)
\(=3x\left(x+4\right)\cdot\left(x-3\right)\)
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\(x^2+5x-6\\ =x^2-x+6x-6\\ =x\left(x-1\right)+6\left(x-1\right)\\ =\left(x+6\right)\left(x-1\right)\\ ---\\ 5x^2+5xy-x-y\\ =x\left(5x-1\right)+y\left(5x-1\right)\\ =\left(5x-1\right)\left(x+y\right)\\ ----\\ 7x-6x^2-2\\ =-6x^2+3x+4x-2\\ =-3x\left(2x-1\right)+2\left(2x-1\right)\\ =\left(2-3x\right)\left(2x-1\right)\)
\(x^2+5x-6=\left(x-1\right)\left(x+6\right)\\ 5x^2+5xy-x-y=\left(5x-1\right)\left(x+y\right)\\ 7x-6x^2-2=\left(3x-2\right)\left(2x-1\right)\)
x^2 + 5x -6
= x^2 + 5x - (5+1)
= x^2 + 5x -5 -1
= 5(x-1) + (x^2 -1)
= 5(x-1) + (x-1) (x+1)
= (5+x+1) (x-1)
5x^2 + 5xy -x-y
= 5x(x+y) - (x+y)
= (5x -1) (x+y)
7x - 6x^2 - 1 (câu này tớ tự ý sửa đề chút ^^!)
= 6x + x - 6x^2 -1
= 6x (1-x) - (1-x)
= (6x -1) (1-x)
x2 + 5x - 6= x2 - x + 6x -6= x(x-1) + 6(x-1)= (x+6)(x-1)
5x2 + 5xy - x - y= 5x2 - x + 5xy - y= x(5x-1) + y(5x - 1)= ( x +y)( 5x -1)
7x - 6x2 - 2= -6x2 + 3x + 4x -2= -3x(2x - 1) + 2(2x -1)= (2 - 3x)(2x-1)