Question

Phân tích đa thức thành nhân tử chung

a) x⁴ + x³ + x +1

b) x⁴ - x³ - x² +1

c) x²y + xy - x - y

d) ax² + a²y - 7x - 7y

e) ax² + ay - bx² - by

f) x( x + 1 )² + x( x - 5 ) - 5( x + 1 )²

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Answer 1

a) \(x^4+x^3+x+1\)

\(\left(x^4+x^3\right)+\left(x+1\right)\)

\(x^3\left(x+1\right)\)+(x+1)

(x+1)(\(x^3+1\))

Answer 2

e)\(ax^2+ay-bx^2-by\)

\(\left(ax^2+ay\right)-\left(bx^2+by\right)\)

\(a\left(x^2+y\right)-b\left(x^2+y\right)\)

\(\left(x^2+y\right)\left(a-b\right)\)

Answer 3

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

\(=\left(x-1\right)\left(x^3-x-1\right)\)

f: \(=\left(x+1\right)^2\left(x-5\right)+x\left(x-5\right)\)

\(=\left(x-5\right)\left(x^2+3x+1\right)\)