Question

[Tạ Phương Linh]

Phân tích đa thức thành nhân tử:

a, 3x^2 +2x

b, 5x - 5y + ax - ay

c, 4x^2 - 25

d,x^2 +6x +5

e, x^2 - y^2 + 2y -1

f, x^3 - 3x + 2

Answer 1

[Lê Ng Hải Anh]

\(a,3x^2+2x=x\left(3x+2\right)\)

\(b,5x-5y+ax-ay=5\left(x-y\right)+a\left(x-y\right)=\left(x-y\right)\left(5+a\right)\)

\(c,4x^2-25=\left(2x-5\right)\left(2x+5\right)\)

\(d,x^2+6x+5=x^2+x+5x+5=x\left(x+1\right)+5\left(x+1\right)=\left(x+1\right)\left(x+5\right)\)

\(e,x^2-y^2+2y-1=x^2-\left(y^2-2y+1\right)=x^2-\left(y-1\right)^2=\left(x-y+1\right)\left(x+y-1\right)\)

Answer 2

[Sắc màu]

a ) 3x² + 2x

= x. ( 3x + 2 )

b ) 5x - 5y + ax - ay

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

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

= ( 5 + a ) ( x - y ) 

c ) 4x² - 25

= ( 2x + 5 ) ( 2x - 5 )

d ) x² + 6x + 5

= x² + x + 5x + 5

= x.( x + 1 ) + 5.( x + 1 )

= ( x + 1 ) ( x + 5 )

e ) x² - y² + 2y - 1

= x² - ( y - 1 )²

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

f ) x³ - 3x + 2

= x³ + 2x² - 2x² - 4x + x + 2

= x² ( x + 2 ) - 2x ( x + 2 ) + ( x + 2 )

= ( x + 2 ) ( x² - 2x + 1 )

= ( x + 2 ) ( x - 1 )²