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\(x^3+x+2\)
\(=x^3-x+2x+2\)
\(=x\left(x^2-1\right)+2\left(x+1\right)\)
\(=\left(x-1\right)x\left(x+1\right)+2\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-x+2\right)\)
\(x^3+3x^2-4\)
\(=x^3-x^2+4x^2-4\)
\(=x^2\left(x-1\right)+4\left(x^2-1\right)\)
\(=x^2\left(x-1\right)+4\left(x-1\right)\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2+4x+4\right)\)
\(=\left(x-1\right)\left(x+2\right)^2\)
3x2 - 7x - 10
= 3x2 + 3x - 10x - 10
= (3x2 + 3x) - (10x + 10)
= 3x(x + 1) - 10(x + 1)
= (3x - 10)(x + 1)
5x3 - 5x2y - 10x2 + 10xy
= 5x(x2 - xy - 2x + 2y)
= 5x[(x2 - xy) - (2x - 2y)]
= 5x[x(x - y) - 2(x - y)]
= 5x(x - 2)(x - y)
chúc bn hok tốt
nhớ ủng hộ tik cho mik nhé! ko lần sau mik ko giúp đâu
có j ko hiểu thì bn cứ bình luận ở dưới nhé
a: =(x+6)(x-1)
n: \(=4x^4+36x^2+81-36x^2\)
\(=\left(2x^2+9-6x\right)\left(2x^2+9+6x\right)\)
=x4-4x3-2x2+12x+9
=x4+x3-5x3-5x2+3x2+3x+9x+9
=x3(x+1)-5x2(x+1)+3x(x+1)+9(x+1)
=(x+1)(x3-5x2+3x+9)
=(x+1)(x3+x2-6x2-6x+9x+9)
=(x+1)(x2(x+1)-6x(x+1)+9(x+1))
=(x+1)(x+1)(x2-6x+9)
=(x+1)2(x-3)2
\(=6x\left(x+2y\right)+5\left(x+2y\right)=\left(6x+5\right)\left(x+2y\right)\)
\(=6x^3\left(x-2\right)+17x^2\left(x-2\right)-4x\left(x-2\right)-3\left(x-2\right)\)
\(=\left(6x^3+17x^2-4x-3\right)\left(x-2\right)\)
\(=\left[6x^2\left(x+3\right)-x\left(x+3\right)-\left(x+3\right)\right]\left(x-2\right)\)
\(=\left(x-2\right)\left(x+3\right)\left(6x^2-x-1\right)\)
\(=\left(x-2\right)\left(x+3\right)\left[2x\left(3x+1\right)-\left(3x+1\right)\right]\)
\(=\left(x-2\right)\left(x+3\right)\left(2x-1\right)\left(3x+1\right)\)
x^3 - x + 3x^2y + 3xy^2 + y^3 - y
=x3+y3+3x2y+3xy2-x-y
=(x+y)(x2-xy+y2)+3xy(x+y)-(x+y)
=(x+y)(x2-xy+y2+3xy-1)
=(x+y)(x2+2xy+y2-1)
=(x+y)[(x+y)2-1]
=(x+y)(x+y-1)(x+y+1)
x^2 + 5x - 6
=x2-x+6x-6
=x.(x-1)+6.(x-1)
=(x-1)(x+6)
phan tich cac da thuc sau thanh nhan tu theo mau:
a)\(2x^3-x\)
\(=x\left(2x^2-1\right)\)
\(=x\left(\left(\sqrt{2}x\right)^2-1^2\right)\)\
\(=x\left(\sqrt{2}x-1\right)\left(\sqrt{2}x+1\right)\)
b)\(5x^2\left(x-1\right)-15x\left(x-1\right)\)
\(=\left(5x^2-15x\right)\left(x-1\right)\)
\(=5x\left(x-3\right)\left(x-1\right)\)
d)\(3x\left(x-2y\right)+6y\left(2y-x\right)\)
\(=3x\left(x-2y\right)-6y\left(x-2y\right)\)
\(=\left(3x-6y\right)\left(x-2y\right)\)
\(=3\left(x-2y\right)\left(x-2y\right)\)
\(=3\left(x-2y\right)^2\)
\(x^2+5x-6=x^2+x-6x-6=x\left(x+1\right)-6\left(x+1\right)=\left(x+1\right)\left(x-6\right)\)
\(2x^2+3x-5=2x^2-2x+5x-5=2x\left(x-1\right)+5\left(x-1\right)=\left(2x+5\right)\left(x-1\right)\)
\(7x-6x^2-2=3x-6x^2+4x-2=-3x\left(2x-1\right)+2\left(2x-1\right)=\left(2-3x\right)\left(2x-1\right)\)
\(16x-5x^2-3=15x-5x^2+x-3=-5x\left(x-3\right)+\left(x-3\right)=\left(1-5x\right)\left(x-3\right)\)