Question

phân tích đa thức thành nhân tử 

a x² + 4x -y² + 4 

b 2x² -18 

c x³ -x² -x + 1 

d x² -7xy + 10y²

Answer 1

a, \(x^2\) + 4\(x\) - y² + 4

= (\(x^2\) + 4\(x\) + 4) - y²

= (\(x\) + 2)² - y²

= (\(x\) + 2 - y)(\(x\) + 2 + y)

Answer 2

b, 2\(x^2\) - 18

= 2.(\(x^2\) -9)

= 2.(\(x\) -3).(\(x\) + 3)

 

Answer 3

c, \(x^3\) - \(x^2\) - \(x\) + 1

= (\(x^3\) + 1) - (\(x^2\) +  \(x\))

= (\(x\) + 1)(\(x\)² - \(x\) + 1) - \(x\).(\(x\) + 1)

=(\(x\) + 1).(\(x^2\) - \(x\) + 1  - \(x\))

= (\(x\) + 1).(\(x\) - 1)²

Answer 4

d, \(x^2\) - 7\(xy\) + 10y²

= (\(x^2\) - 7\(xy\) + \(\dfrac{49}{4}\)y²) - \(\dfrac{9}{4}\)y²

= (\(x\) - \(\dfrac{7}{2}\)y)² - \(\dfrac{9}{4}\)y²

= (\(x\) - \(\dfrac{7}{2}\)y - \(\dfrac{3}{2}\)y).(\(x\) - \(\dfrac{7}{2}\)y + \(\dfrac{3}{2}\)y)

= (\(x\) - 5y).(\(x\) - 2y)