a) a⁴ + a² - 2

a⁴ + 2a² - a² - 2

a².( a² + 2 ) - ( a² + 2 )

( a² - 1 ).( a² + 2 )

( a + 1 ).( a - 1 ).( a² +2 )

b) x⁴ + 4x² - 5

x⁴ + 5x² - x² - 5

x².( x² + 5 ) - ( x² + 5 )

( x² - 1 ).( x² + 5 )

( x + 1 ).( x - 1 ).( x² + 5 )

c) x³ - 19x - 30

x³ + 2x² - 2x² + 4x - 15x - 30

x²( x + 2 ) - 2x.( x + 2 ) - 15.( x + 2 )

( x + 2 ).( x² - 2x - 15 )

d) x³ - 7x - 6

x³ - 3x² + 3x² - 9x + 2x - 6

x².( x - 3 ) + 3x.( x - 3 ) + 2.( x - 3 )

( x - 3 ).( x² + 3x +2 )

( x - 3 ).( x² + 2x + x + 2 )

( x - 3 ).( x.( x + 2 ) + ( x + 2 )

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

e) x³ - 5x² - 14x

x³ - 7x² + 2x² - 14x

x².( x - 7 ) + 2x.( x - 7 )

( x - 7 ).( x² + 2x )

x.( x + 2 ).( x - 7 )

(x - 4)(x² + 4x + 16) - x(x² - 6) = 2

x³ - 64 - x³ + 6x = 2

6x = 2 + 64

6x = 66

x = 66 : 6

x = 11

x³ - 27 + 3x(x - 3)

= (x - 3)(x² + 3x + 9) + 3x(x - 3)

= (x - 3)(x² + 3x + 9 + 3x)

= (x - 3)(x² + 6x + 9)

= (x - 3)(x + 3)²

5x³ - 7x² + 10x - 14

= 5x(x² + 2) - 7(x² + 2)

= (x² + 2)(5x - 7)

a)x^2-(a+b)x+ab

= x^2 - ax - bx + ab

= (x^2 - ax) - (bx - ab)

= x(x-a) - b(x-a)

= (x-b)(x-a) 

b)7x^3-3xyz-21x^2+9z

= 

c)4x+4y-x^2(x+y)

= 4(x + y) - x^2(x+y)

= (4-x^2) (x+y)

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

d) y^2+y-x^2+x

= (y^2 - x^2) + (x+y)

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

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

e)4x^2-2x-y^2-y

= [(2x)^2 - y^2] - (2x +y)

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

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

f)9x^2-25y^2-6x+10y

= 

ko biết làm

Ta có : 5x³ - 45x

= 5x(x² - 9)

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

b ) Ta có : 3x² - 7x - 6 

= 3x² - 9x + 2x - 6 

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

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

Bài 4.

a) 3xy² - 45x²y = 3xy( y - 15x )

b) 25y² - 4x² + 4x - 1

= 25y² - ( 4x² - 4x + 1 )

= ( 5y )² - ( 2x - 1 )²

= ( 5y - 2x + 1 )( 5y + 2x - 1 )

c) x² - 5x + xy - 5y

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

= ( x - 5 )( x + y )

d) x² - 8x - 33

= x² + 3x - 11x - 33

= x( x + 3 ) - 11( x + 3 )

= ( x + 3 )( x - 11 )

Bài 5.

a) A = ( x - 2 )³ - x²( x - 4 ) + 8

= x³ - 6x² + 12x - 8 - x³ + 4x² + 8

= -2x² + 12x

B = ( x² - 6x + 9 ) : ( x - 3 ) - x( x + 7 ) - 9

= ( x - 3 )² : ( x - 3 ) - x² - 7x - 9

= x - 3 - x² - 7x - 9

= -x² - 6x - 12

b) Với x = -1 thì A = -2.(-1)² + 12.(-1) = -2 - 12 = -14

a, ( x² + x )² - 14 ( x² + x ) + 24

= (x² + x)² - 2(x² + x) -12(x² + x) + 24

= (x² + x).(x² + x -2) - 12(x² + x -2)

= (x² + x -2).(x² + x -12)

= (x² + 2x - x - 2).(x² + 4x - 3x - 12)

=[x.(x+2)-(x+2)].[x.(x+4)-3(x+4)]

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

= x⁴ + 2x³ - 13x² - 14x + 24

b, ( x² + x )² + 4x² + 4x - 12

= x⁴ + 2x³ + x² + 4x² + 4x -12

= x⁴ + 2x³ + 5x² + 4x -12

c, x⁴ + 2x³ + 5x² + 4x - 12

= x⁴ - x³ + 3x³ - 3x² + 8x² - 8x +12x -12

= x³(x-1) + 3x²(x-1) + 8x(x-1) + 12(x-1)

= (x-1) . (x³ + 3x² + 8x +12)

= (x-1) . ( x³ +2x² + x² + 2x + 6x +12)

= (x-1). [x²(x+2) + x(x+2) + 6(x+2)]

= (x-1).(x+2).(x² + x+ 6)

a)x⁷+x⁵+1=x⁷+x⁶-x⁶+2x⁵-x⁵+x⁴-x⁴+x³-x³+x²-x²+1

=x⁷-x⁶+x⁵-x³+x²+x⁶-x⁵+x⁴-x²+x+x⁵-x⁴+x³-x+1

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

=(x²+x+1)(x⁵-x⁴+x³-x+1)

b)4x⁴-32x²+1=4x⁴+12x³+2x²-12x³-36x²-6x+2x²+6x+1

=2x²(2x²+6x+1)-6x(2x²+6x+1)+1(2x²+6x+1)

=(2x²-6x+1)(2x²+6x+1)

c)x⁶+27=(x²+3)(x²-3x+3)(x²+3x+3)

d)3(x⁴+x²+1)-(x²+x+1)

=3x⁴-3x³+2x²+3x³-3x²+2x+3x²-3x+2

=x²(3x²-3x+2)+x(3x²-3x+2)+1(3x²-3x+2)

=(x²+x+1)(3x²-3x+2)

e)bạn tự làm nhé

\(x^8+x^7+1\)

\(=x^8+x^7+x^6-x^6+x^5-x^5+x^4-x^4+x^3-x^3+x^2-x^2+x-xx+1\)

\(=\left(x^8-x^6+x^5-x^3+x^2\right)\)

\(+\left(x^7-x^5+x^4-x^2+x\right)\)

\(+\left(x^6-x^4+x^3-x+1\right)\)

\(=\left(x^2+x+1\right)\left(x^6-x^4+x^3-x+1\right)\)

\(x^5+x+1\)

\(=x^5-x^2+x^2+x+1\)

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

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

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

\(x^4+2x^2-24\)

\(=x^4+2x^2+1-25\)

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

\(=\left(x^2+6\right)\left(x^2-4\right)\)

\(=\left(x^2+6\right)\left(x+2\right)\left(x-2\right)\)

Bài 2 : Phân tích các đa thức sau thành nhân tử :
a, x² + 7x + 12

= x² + 3x + 4x + 12

= x(x + 3) + 4(x + 3)

= (x + 3)(x + 4)
b, 3x² - 8x + 5

= 3x² - 3x - 5x + 5

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

= (x - 1)(3x - 5)
c, x⁴ + 5x² - 6

= x⁴ - x² + 6x² - 6

= x²(x² - 1) + 6(x² - 1)

= (x² - 1)(x² + 6)

= (x - 1)(x + 1)(x² + 6)
d, x⁴ - 34x² + 225

= x⁴ - 9x² - 25x² + 225

= x²(x² - 9) - 25(x² - 9)

= (x² - 9)(x² - 25)

= (x - 3)(x + 3)(x - 5)(x + 5)
e, x² - 5xy + 6y²

= x² + xy - 6xy + 6y²

= x(x + y) - 6y(x + y)

= (x + y)(x - 6y)
f, 4x² - 17xy + 13y²

= 4x² - 4xy - 13xy + 13y²

= 4x(x - y) - 13y(x - y)

= (x - y)(4x - 13y)