Phân tích đa thức x^2+x-6 thành nhân tử

=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)

Phân tích đa thức thành nhân tử
1, x³z + x²yz - x²z² - xyz²
2, x² - ( a + b )xy + aby²
3, ab( x² + y² ) + xy( a² + b² )
4, ( xy + ab )² + ( ay - bx )²
5, a²( b - c ) + b²( c - a ) + c²( a - b )
6, 16x² - 40xy + 25y²
7, 25x⁴ - 10x²y + y²
8, -16x⁴y⁶ - 24x⁵y⁵ - 9x⁶y⁴
9, 16x² - 4y² - 8x + 1
10, 49x² - 25 + 42xy + 9y²

a) sai đề trầm trọng nha bn

b) \(x^4+2x^3+x^2+x+1\)

\(=x^4+x^3+x^3+x^2+x+1\)

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

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

c) \(x^3+6x^2+11x+6\)

\(=x^3+x^2+5x^2+5x+6x+6\)

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

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

\(=\left(x+1\right)\left(x^2+2x+3x+6\right)\)

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

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

\(1.\)

\(x^3z+x^2yz-x^2z^2-xyz^2\)

\(=x^3z-x^2z^2+x^2yz-xyz^2\)

\(=x^2z\left(x-z\right)-xyz\left(x-z\right)\)

\(=\left(x^2z-xyz\right)\left(x-z\right)\)

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

\(2.\)

\(x^2-\left(a+b\right)xy+aby^2\)

\(=x^2-axy-bxy+aby^2\)

\(=x^2-bxy-axy+aby^2\)

\(=x\left(x-by\right)-ay\left(x-by\right)\)

\(=\left(x-ay\right)\left(x-by\right)\)

\(3.\)

\(ab\left(x^2+y^2\right)+xy\left(x^2+y^2\right)\)

\(=abx^2+aby^2+a^2xy+b^2xy\)

\(=abx^2+b^2xy+a^2xy+aby^2\)

\(=bx\left(ax+by\right)+ay\left(ax+by\right)\)

\(=\left(ax+by\right)\left(bx+ay\right)\)

\(4.\)

\(\left(xy+ab\right)^2+\left(ay-bx\right)^2\)

\(=x^2y^2+2abxy+a^2b^2+a^2y^2-2aybx+b^2x^2\)

\(=x^2y^2+a^2b^2+a^2y^2+b^2x^2\)

\(=x^2y^2+b^2x^2+a^2b^2+a^2y^2\)

\(=x^2\left(b^2+y^2\right)+a^2\left(b^2+y^2\right)\)

\(=\left(a^2+x^2\right)\left(b^2+y^2\right)\)

\(5.\)

\(a^2\left(b-c\right)+b^2\left(c-a\right)+c^2\left(a-b\right)\)

\(=a^2b-a^2c+b^2c-ab^2+ac^2-bc^2\)

\(=a^2b-ab^2-a^2c-b^2c+ac^2-bc^2\)

\(=ab\left(a-b\right)-c\left(a^2-b^2\right)+c^2\left(a-b\right)\)

\(=ab\left(a-b\right)-c\left(a-b\right)\left(a+b\right)+c^2\left(a-b\right)\)

\(=\left(a-b\right)\left(ab-ac-bc+c^2\right)\)

\(=\left(a-b\right)\left(ab-bc-ac+c^2\right)\)

\(=\left(a-b\right)\left[b\left(a-c\right)-c\left(a-c\right)\right]\)

\(=\left(a-c\right)\left(b-c\right)\left(a-c\right)\)

\(=\left(a-b\right)\left(a-c\right)\left(b-c\right)\)

\(6.\)

\(16x^2-40xy+2y^2\)

\(=\left(4x\right)^2-2\cdot4\cdot5xy+\left(5y\right)^2\)

\(=\left(4x-5y\right)^2\)

\(7.\)

\(25x^4-10x^2y+y^2\)

\(=\left(5x^2\right)^2-2\cdot5x^2y+y^2\)

\(=\left(5x^2+y\right)^2\)

\(8.\)

\(-16x^4y^6-24x^5y^5-9x^6y^4\)

\(=-\left(4^2x^4y^6+2\cdot4\cdot3x^5y^5+3^2x^6y^4\right)\)

\(=-\left[\left(4x^2y^3\right)^2+2\left(4x^2y^3\right)\left(3x^3y^2\right)+\left(3x^3y^2\right)^2\right]\)

\(=\left(4x^2y^3+3x^3y^2\right)^2\)

\(9.\)

\(16x^2-4y^2-8x+1\)

\(=\left(4x\right)^2-\left(2y\right)^2-8x+1\)

\(=\left(4x\right)^2-8x+1-\left(2y\right)^2\)

\(=\left(4x+1\right)^2-\left(2y\right)^2\)

\(=\left(4x-2y+1\right)\left(4x+2y+1\right)\)

\(10.\)

\(49x^2-25+42xy+9y^2\)

\(=\left(7x\right)^2-5^2+2\cdot7\cdot3xy+\left(3y\right)^2\)

\(=\left(7x\right)^2+2\cdot7\cdot3xy+\left(3y\right)^2-5^2\)

\(=\left(7x+3y\right)^2-5^2\)

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

Phân tích thành nhân tử ( tách các hạng tử )

a, x³+2x³+x²+x+1

b, x⁴+2x³+x²+x+1

c, x³+6x²+11x+6