a,x² - 13x + 36

= x² - 4x - 9x + 36

= x(x - 4) - 9(x - 4)

= (x - 4)(x - 9)

b,x² + 3x - 18

= x² - 9 + 3x - 9

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

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

= (x - 3)(x + 6)

c,x² - 5x - 24

= x² + 3x - 8x - 24

= x(x + 3) - 8(x + 3)

= (x + 3)(x - 8)

d,3x² - 16x + 5

= 3x² - 15x - x + 5

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

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

e, 8x² + 30x + 7

= 8x² + 2x + 28x + 7

= 2x(4x + 1) + 7(4x + 1)

= (4x + 1)(2x + 7)

g,2x² - 5x - 12

= 2x² - 8x + 3x - 12

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

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

i,x⁴ + 4

= x⁴ + 4x² + 4 - 4x²

= (x² + 2)² - (2x)²

= (x² + 2 - 2x)(x² + 2 + 2x)

Phân tích đa thức thành nhân tử bằng cách tách một số hạng tử thành nhiều số hạng khác

a) x^2+4x+3

b) 4x^2-4x-3

c)x^2-x-12

d) 4x^4-4x^2-8y^4

a, 5x^2 +5xy - x - y 

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

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

b, 2x^2  + 3x - 5 

= 2x^2 - 2x + 5x - 5 

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

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

c; 16x - 5x^2 - 3 

c, = - ( 5x^2 - 16x + 3 )

   = - ( 5x^2 - x - 15x + 3 )

= - [ x(5x - 1 ) - 3 (5x - 1) ]

= - ( x- 3)(5x -  1 )

`@` `\text {Ans}`

`\downarrow`

`x^2 + 4x + 3`

`= x^2 + 3x + x + 3`

`= (x^2 + 3x) + (x + 3)`

`= x(x + 3) + (x + 3)`

`= (x+1)(x+3)`

____

`2x^2 + 3x - 5`

`= 2x^2 + 5x - 2x - 5`

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

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

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

____

`16x - 5x^2 - 3`

`= 15x + x - 5x^2 - 3`

`= (15x - 5x^2) + (x - 3)`

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

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

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

\(x^2+4x+3=x^2+3x+x+3=x\left(x+3\right)+\left(x+3\right)=\left(x+1\right)\left(x+3\right)\\----\\ 2x^2+3x-5=2x^2-2x+5x-5=2x\left(x-1\right)+5\left(x-1\right)=\left(2x+5\right)\left(x-1\right)\\ ----\\ 16x-5x^2-3=-5x^2+15x+x-3=-5x\left(x+3\right)-\left(x+3\right)=-\left(5x+1\right)\left(x+3\right)\)

\(x^2+4x+3=\left(x+1\right)\left(x+3\right)\\ 2x^2+3x-5=\left(2x+5\right)\left(x-1\right)\\ 16x-5x^2-3=\left(1-5x\right)\left(x-3\right)\)

a)

ta có \(x^2+8x+7\)

\(=x^2+7x+x+7\)

\(=x\left(x+7\right)+\left(x+7\right)\)

\(=\left(x+7\right)\left(x+1\right)\)

b)

Ta có \(8x^2+30x+7\)

\(=8x^2+2x+28x+7\)

\(=2x\left(4x+1\right)+7\left(4x+1\right)\)

\(\left(4x+1\right)\left(2x+7\right)\)

A)(x+1)(x+7)

B)(x+1/4)(x+7/2)

giải rõ hơn dc không bạn ??

a)\(=\left(x-2\right)\left(5x-3x^2\right)\)

\(=x\left(x-2\right)\left(5-3x\right)\)

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

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

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

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

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

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

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

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

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

e)\(=[\left(x^2\right)^2+8^2+2.x^2.8]-2.8.x^2\)

\(=\left(x^2+8\right)^2-16x^2\)

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

__Chúc bạn hc tốt ......

a.\(3x^3-x^2-21x+7=\)\(x^2\left(3x-1\right)-7\left(3x-1\right)=\left(3x-1\right)\left(x^2-7\right)\)

b.\(x^3-4x^2+8x-8=\left(x^3-8\right)+\left(-4x^2+8x\right)\)=\(\left(x-2\right)\left(x^2+2x+4\right)\)\(-\)\(4x\left(x-2\right)\)

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

c.\(x^3-5x^2-5x+1\)=\(\left(x^3+1\right)-\left(5x^2+5x\right)\)=\(\left(x+1\right)\left(x^2-x+1\right)-5x\left(x+1\right)\)

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

1)x²-8x-9

= x^2 - 9x +x -9

= x(x+1) - 9 (x+1)

= (x-9) (x+1)

2)x²+3x-18

3)x³-5x²+4x

=x^3 - 4x^2 - x^2 + 4x 

= x^2 (x-1) - 4x(x-1)

= (x^2 - 4x) (x-1)

= x(x-4)(x-1)

4)x³-11x²+30x

5)x³-7x-6

6)x¹⁶-64

\(=\left(x^8\right)^2-8^2\)

\(=\left(x^8-8\right)\left(x^8+8\right)\)

7)x³-5x²+8x-4

8)x²-3x+2

= x^2 - 2x - x +2

= x(x-1) -2(x-1)

= (x-2)(x-1)

1)   \(\left(x-9\right)\left(x+1\right)\)             2)   \(\left(x-3\right)\left(x+6\right)\)                                           3)   \(x\left(x-4\right)\left(x-1\right)\)

4)    \(x\left(x-6\right)\left(x-5\right)\)         5)\(\left(x-3\right)\left(x+1\right)\left(x+2\right)\)                               6)   ........

7)  \(\left(x-1\right)\left(x-2\right)\left(x-2\right)\)          8)   \(\left(x-2\right)\left(x-1\right)\)

a) \(39x-39y=39\left(x-y\right)\)

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

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

c) \(16x^2+24xy+9y^2=\left(4x\right)^2+4x.3y.2+\left(3y\right)^2=\left(4x+3y\right)^2\)

d) \(25x^2-\frac{1}{25y^2}=\left(5x\right)^2-\left(\frac{1}{5y}\right)^2=\left(5x-\frac{1}{5y}\right)\left(5x+\frac{1}{5y}\right)\)

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

f) \(5x^2-45y^2-30y-5=5\left(x^2-9y^2-6y-1\right)=5\left[x^2-\left(9y^2+6y+1\right)\right]\)

\(=5\left[x^2-\left(3y+1\right)^2\right]=5\left(x-3y-1\right)\left(x+3y+1\right)\)

g) \(x^2+2x+1-y^2-4y-1=\left(x^2+2x+1\right)-\left(y^2+2y+1\right)\) ( Chắc đề vậy :v ) 

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

h) \(4x^2+8x-5=4x^2-2x+10x-5=2x\left(2x-1\right)+5\left(2x-1\right)\)

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