Question

phân tích đa thức sau thành nhân tử 

h) 16x-5x^2-3

i) x^3-4x

l) x^2-y^2-5x+5y

e) x^2+4x+3

f) x^3-x+3x^2y+3xy^2+y^3-y

Answer 1

h) 16x - 5x² - 3

= -5x² + 16x - 3

= -5x² - 15x - x - 3

= (-5x² - 15x) - (x + 3)

= -5x(x + 3) - (x + 3)

= (x + 3)(-5x - 1)

i) x³ - 4x

= x(x² - 4)

= x(x - 2)(x + 2)

l) x² - y² - 5x - 5y

= (x² - y²) - (5x + 5y)

= (x - y)(x + y) - 5(x + y)

= (x + y)(x - y - 5)

e) x² + 4x + 3

= x² + x + 3x + 3

= (x² + x) + (3x + 3)

= x(x + 1) + 3(x + 1)

= (x + 1)(x + 3)

f) x³ - x + 3x²y + 3xy² + y³ - y

= (x³ + 3x²y + 3xy² + y³) - (x + y)

= (x + y)³ - (x + y)

= (x + y)[(x + y)² - 1]

= (x + y)(x + y - 1)(x + y + 1)

Answer 2

h: \(=-\left(5x^2-16x+3\right)=-\left(5x^2-15x-x+3\right)\)

\(=-\left(x-3\right)\left(5x-1\right)\)

i: \(=x\left(x^2-4\right)=x\left(x-2\right)\left(x+2\right)\)

j: \(=\left(x-y\right)\left(x+y\right)-5\left(x-y\right)=\left(x-y\right)\left(x+y-5\right)\)

e: \(=\left(x+1\right)\left(x+3\right)\)

f: \(=\left(x+y\right)^3-\left(x+y\right)\)

\(=\left(x+y\right)\left(x+y+1\right)\left(x+y-1\right)\)