Question

Phân tích các đa thức sau thành nhân tử (bằng phương pháp đặt nhân tử chung)

  a) 4x(2y - z) + 7y(z - 2y)

  b) 2x(x + 3) + (3 + x)

  c) 3x(2x - 1) + 7x²(1 = 2x)

  d) y(x - z) + 7(z - x)

Answer 1

a) Ta có: \(4x\left(2y-z\right)+7y\left(z-2y\right)\)

        \(=4x\left(2y-z\right)-7y\left(2y-z\right)\)

        \(=\left(4x-7y\right)\left(2y-z\right)\)

Answer 2

b) Ta có: \(2x\left(x+3\right)+\left(3+x\right)\)

        \(=\left(2x+1\right)\left(x+3\right)\)

Answer 3

c) Ta có: \(3x\left(2x-1\right)+7x^2\left(1-2x\right)\)

        \(=3x\left(2x-1\right)-7x^2\left(2x-1\right)\)

        \(=\left(3x-7x^2\right)\left(2x-1\right)\)

Answer 4

d) Ta có: \(y\left(x-z\right)+7\left(z-x\right)\)

        \(=y\left(x-z\right)-7\left(x-z\right)\)

        \(=\left(y-7\right)\left(x-z\right)\)

Answer 5

a) 4x( 2y - z ) + 7y( z - 2y )

= 4x( 2y - z ) - 7y( 2y - z )

= ( 2y - z )( 4x - 7y )

b) 2x( x + 3 ) + ( 3 + x )

= 2x( x + 3 ) + ( x + 3 )

= ( x + 3 )( 2x + 1 )

c) 3x( 2x - 1 ) + 7x²( 1 - 2x )

= 3x( 2x - 1 ) - 7x²( 2x - 1 )

= ( 2x - 1 )( 3x - 7x² )

= ( 2x - 1 )x( 3 - 7x )

d) y( x - z ) + 7( z - x )

= y( x - z ) - 7( x - z )

= ( x - z )( y - 7 )