=x^2+3x-2x-6

=(x^2+3x)-(2x+6)

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

=(x-2)(x+3)

Phân tích đa thức thành nhân tử

2x4+3x3-12x2-7x+6

2x4 + 3x3 - 12x2 - 7x + 6

= 2x4 - 4x3 + 7x3 - 14x2 + 2x2 - 4x - 3x + 6

= (2x4 - 4x3) + (7x3 - 14x2) + (2x2 - 4x) - (3x - 6)

= 2x3(x - 2) + 7x2(x - 2) + 2x(x - 2) - 3(x - 2)

= (2x3 + 7x2 + 2x - 3)(x - 2)

= (2x3 - x2 + 8x2 - 4x + 6x - 3)(x - 2)

= [(2x3 - x2) + (8x2 - 4x) + (6x - 3)](x - 2)

= [x2(2x - 1) + 4x(2x - 1) + 3(2x - 1)](x - 2)

= (x2 + 4x + 3)(x - 1)(x - 2)

= (x2 + x + 3x + 3)(x - 1)(x - 2)

= [(x2 + x) + (3x + 3)](x - 1)(x - 2)

= [x(x + 1) + 3(x + 1)](x - 1)(x - 2)

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

= (x + 3)(x + 2)(x2 - 1)

NHỚ TIK MIK NHÉ

Phân tích đa thức thành nhân tử:

2x^2 - 13x - 24

3x^2 + 16x + 5
15x^2 + x - 28
35x^2 - 18y^2 + 83xy
6x^2 - 7x - 49
15x^2 - 22x - 5
2x^2 - 3x - 9

*) \(2x^2-13x-24=2x^2+3x-16x-24\)

\(=x\left(2x+3\right)-8\left(2x+3\right)=\left(x-8\right)\left(2x+3\right)\)

*) \(3x^2+16x+5=3x^2+x+15x+5\)

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

*) \(15x^2+x-28=15x^2-20x+21x-28\)

\(=5x\left(3x-4\right)+7\left(3x-4\right)=\left(5x+7\right)\left(3x-4\right)\)

*) \(35x^2-18y^2+83xy=35x^2-7xy+90xy-18y^2\)

\(=7x\left(5x-y\right)+18y\left(5x-y\right)=\left(7x+18y\right)\left(5x-y\right)\)

*) \(6x^2-7x-49=6x^2+14x-21x-49\)

\(=2x\left(3x+7\right)-7\left(3x+7\right)=\left(2x-7\right)\left(3x+7\right)\)

*) \(15x^2-22x-5=15x^2+3x-25x-5\)

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

*) \(2x^2-3x-9=2x^2+3x-6x-9\)

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

Cách 2 .

x7 + x5 + 1

= x7 + x6 + x5 - x6 + 1

= x5( x2 + x + 1) - [ ( x3 )2 - 1]

= x5( x2 + x + 1) - ( x3 - 1)( x3 + 1)

= x5( x2 + x + 1) -( x - 1)( x2 + x + 1)( x3 + 1)

= ( x2 + x + 1)[ x5 -( x - 1)( x3 + 1)]

= (x2 + x + 1)( x5 - x4 + x3 - x + 1)

2xy - x^2 - y^2 + 16

Phân tích đa thức sau thành nhân tử: \(x^7+x^5+1\)

Các bạn làm ơn giúp mik mik nhanh nhanh nha mấy bạn! Mik cảm ơn các bạn rất nhiều ạ!

2xy-x2-y2+16

=-x2+2xy-y2+16

=-(x2-2xy+y2)+16

=-(x-y)2+16

=(x-y)2-16

=(x-y)2-42

=(x-y-4)(x-y+4)