Question

Đặt nhân tử :
a) x^3-16x

b) x^3-3x^2-4x

c) x^2-y^2+2x+1

d) ax^2+ay-bx^2-by

e) 2x^3-4x^2+x-2

Answer 1

\(a.x^3-16x=x\left(x^2-16\right)=x\left(x-4\right)\left(x+4\right)\)

\(b.x^3-3x^2-4x=x^3+x^2-4x^2-4x=x^2\left(x+1\right)-4x\left(x+1\right)=\left(x+1\right)\left(x^2-4x\right)=x\left(x+1\right)\left(x-4\right)\)\(c.x^2-y^2+2x+1=\left(x+1\right)^2-y^2=\left(x+1-y\right)\left(x+1+y\right)\)

\(d.ax^2+ay-bx^2-by=a\left(x^2+y\right)-b\left(x^2+y\right)=\left(a-b\right)\left(x^2+y\right)\)\(e.2x^3-4x^2+x-2=2x^2\left(x-2\right)+\left(x-2\right)=2x^2\left(x-2\right)\)

Answer 2

Giải:

a) \(x^3-16x=x\left(x^2-16\right)=x\left(x-4\right)\left(x+4\right)\)

b) \(x^3-3x^2-4x=x\left(x^2-3x-4\right)=x\left(x+4\right)\left(x-1\right)\)

c) \(x^2-y^2+2x+1=\left(x+1\right)^2-y^2=\left(x+1-y\right)\left(x+1+y\right)\)

d) \(ax^2+ay-bx^2-by=a\left(x^2+y\right)-b\left(x^2+y\right)=\left(a-b\right)\left(x^2+y\right)\)

e) \(2x^3-4x^2+x-2=2x^2\left(x-2\right)+\left(x-2\right)=\left(2x^2+1\right)\left(x-2\right)\)

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