a) 8x^2 - 2x - 1
=8x2+2x-4x-1
=2x(4x+1)-(4x+1)
=(2x-1)(4x+1)
b) 6x^2 + 7xy + 2y^2
=4xy+6x2+4y2+3xy
=2x(2y+3x)+y(2y+3x)
=(2y+3x)(y+2x)
c) chịu
d)x^3 + x + 2
Ta thấy :x=-1 là nghiệm của đa thức (đây là dùng pp nhẩm nghiệm nhé)
=>đa thức có 1 hạng tử là x+1
=>(x+1)(x2-x+2) (nếu bn cần cách khác thì nhắn vs mk)
e) x^3 - 2x - 1
lí luận tương tự phần d
=>(x+1)(x2-x-1)
f) x^3 + 3x^2 - 4
lí luận tương tự phần d
=(x-1)(x2+4x+4)
=(x-1)(x+2)2
g) x^2 - 15x + 14
=x2-x-14x+14
=x(x-1)-14(x-1)
=(x-14)(x-1)
a) \(8x^2-2x-1=\left(4x^2-2x\right)+\left(4x^2-1\right)=2x\left(2x-1\right)+\left(2x-1\right)\left(2x+1\right)=\left(2x-1\right)\left(4x+1\right)\)
b) \(6x^2+7xy+2y^2=\left(6x^2+3xy\right)+\left(4xy+2y^2\right)=3x\left(2x+y\right)+2y\left(2x+y\right)=\left(2x+y\right)\left(3x+2y\right)\)
c) \(9x^2-9xy-4y^2=\left(9x^2-y^2\right)-\left(9xy+3y^2\right)=\left(3x-y\right)\left(3x+y\right)-3y\left(3x+y\right)=\left(3x+y\right)\left(3x-4y\right)\)
d) \(x^3+x+2=\left(x^3+1\right)+\left(x+1\right)=\left(x+1\right)\left(x^2-x+1\right)+\left(x+1\right)=\left(x+1\right)\left(x^2-x+2\right)\)
e) \(x^3-2x-1=\left(x^3-x\right)-\left(x+1\right)=x\left(x-1\right)\left(x+1\right)-\left(x+1\right)=\left(x+1\right)\left(x^2-x-1\right)\)
f) \(x^3+3x^2-4=\left(x^3-1\right)+\left(3x^2-3\right)=\left(x-1\right)\left(x^2+x+1\right)+3\left(x-1\right)\left(x+1\right)=\left(x-1\right)\left(x^2+x+1+3x+3\right)=\left(x-1\right)\left(x^2+4x+4\right)=\left(x-1\right)\left(x+2\right)^2\)
g) \(x^2-15x+14=x^2-x+14-14x=x\left(x-1\right)-14\left(x-1\right)=\left(x-1\right)\left(x-14\right)\)
c) 2x2(x +1) + 4x(x +1); d) 2 x(y - 1) - 2