Question

Phân tích đa thức thành nhân tử rồi thực hiện phép chia

a. (3x⁵-9x³+18x):3x

b. (x⁴-x³+x²):x²

c. (x²+2x+1):(x+1)

d. (8x³+27):(2x+3)

e. (x³-3x²+3x-1):(x-1)

Answer 1

a: \(=x^4-3x^2+6\)

b: \(=x^2-x+1\)

c: \(=x+1\)

d: \(=4x^2-6x+9\)

e: \(=x^2-2x+1\)

Answer 2

a, \(\dfrac{3x^5-9x^3+18x}{3x}=3x^2-3x^2+6\)

b, \(\dfrac{x^4-x^3+x^2}{x^2}=x^2-x+1\)

c, \(\dfrac{x^2+2x+1}{x+1}=\dfrac{\left(x+1\right)^2}{x+1}=x+1\)

d, \(\dfrac{8x^3+27}{2x+3}=\dfrac{\left(2x+3\right)\left(4x^2-6x+9\right)}{2x+3}=4x^2-6x+9\)

e, \(\dfrac{x^3-3x^2+3x-1}{x-1}=\dfrac{\left(x-1\right)^3}{x-1}=\left(x-1\right)^2=x^2-2x+1\)

Answer 3

`a)(3x^5-9x^3+18x):3x`

`=3x(x^4-3x^2+6):3x`

`=x^4-3x^2+6`

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`b)(x^4-x^3+x^2):x^2`

`=x^2(x^2-x+1):x^2`

`=x^2-x+1`

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`c)(x^2+2x+1):(x+1)`

`=(x+1)^2:(x+1)`

`=x+1`

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`d)(8x^3+27):(2x+3)`

`=(2x+3)(4x^2+6x+9):(2x+3)`

`=4x^2+6x+9`

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`e)(x^3-3x^2+3x-1):(x-1)`

`=[(x^3-1)-(3x^2-3x)]:(x-1)`

`=[(x-1)(x^2+x+1)-3x(x-1)]:(x-1)`

`=(x-1)(x^2+x+1-3x):(x-1)`

`=x^2+x+1-3x=x^2-2x+1=(x-1)^2`