\(C=x^3+5x^2+8x+4\)

   \(=x^3+x^2+4x^2+4x+4x+4\)

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

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

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

\(D=x^3-x^2-4\)

    \(=x^3-2x^2+x^2-2x+2x-4\)

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

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

Chúc bạn học tốt.

b mk thấy nó sai đề sao ý 

c) \(C=\left(x^2+x+4\right)^2+8x\left(x^2+x+4\right)+15x^2\)

\(=\left(x^2+x+4\right)^2+2.4x.\left(x^2+x+4\right)+16x^2-x^2\)

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

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

\(=\left(x^2+5x+4-x\right)\left(x^2+5x+4+x\right)=\left(x^2+4x+4\right)\left(x^2+6x+4\right)\)

a, 8x²+10x =2x.(4x+5)

b, 4x²-8x+4 =4.(x² -2x+1)=4.(x-1)²

c, 3x² -3xy -5x +5y =(3x²-5x) - (3xy-5y) = x.(3x-5)- y.(3x-5)= (x-y).(3x-5)

d, x²+ 4x- 45=x²+ 9x- 5x- 45= x.(x+9)- 5.(x+9)=(x-5).(x+9)

a , 8 x ² + 10 x

= 2 x ( 4 x + 5 )

b , 4 x ² - 8 x + 4

= ( 2x ) ² - 2 . 2 x . 2 + 2 ²

= ( 2x + 2 ) ²

c ) 3 x ² - 3 x y - 5 x + 5 y

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

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

d ) x ² + 4x - 45

= x ² + 2 x . 2 + 4 - 49

= ( x + 2 ) ² - 49

= ( x + 2 ) ² - 7 ²

= ( x + 2 - 7 ) ( x + 2 + 7)

= ( x - 5 ) ( x + 9 )

a) -3x^2+x+4

=-3x^2-3x+4x+4

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

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

b) \(x^3-3x^2+2\)

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

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

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

c) \(x^4y^4+64\)

\(=x^4y^4+16x^2+64-16x^2\)

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

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

d) \(x^8+x^7+1\)

\(=x^8+x^7+x^6-x^6+1\)

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

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

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

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

mk ghi đáp án, còn lại bạn tự biến đổi

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

b) \(x^3+5x^2+8x+4=\left(x+1\right)\left(x+2\right)^2\)

c) \(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24=\left(x+1\right)\left(x+6\right)\left(x^2+7x+16\right)\)

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

e) \(x^4-7x^3+14x^2-7x+1=\left(x^2-4x+1\right)\left(x^2-3x+1\right)\)

mk làm chi tiết theo yêu của của người hỏi đề:

a) \(2x^3-x^2+5x+3\)

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

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

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

b)  \(x^3+5x^2+8x+4\)

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

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

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

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

c) x² - x + 9x - 9

=(x²-x) +  (9x-9)

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

= (x-1)(x+9)

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

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

d) \(x^2+14x+48=\left(x+7\right)^2-1=\left(x+7+1\right)\left(x+7-1\right)=\left(x+8\right)\left(x+6\right)\)

b)(x²+x+1)(x²+x+2)-12

Đặt t=x²+x+1

t(t+1)-12=t²+t-12

=(t-3)(t+4)=(x²+x+1-3)(x²+x+1+4)

=(x²+x-2)(x²+x+5)

=(x-1)(x+2)(x²+x+5)

c)(x²+8x+7)(x²+8x+15)+15

Đặt t=x²+8x+7 

t(t+8)+15=t²+8t+15

=(t+3)(t+5)

=(x²+8x+7+3)(x²+8x+7+15)

=(x²+8x+10)(x²+8x+22)

d)(x+2)(x+3)(x+4)(x+5)-24

=(x²+7x+10)(x²+7x+12)-24

Đặt t=x²+7x+10

t(t+2)-24=(t-4)(t+6)

=(x²+7x+10-4)(x²+7x+10+6)

=(x²+7x+6)(x²+7x+16)

=(x+1)(x+6)(x²+7x+16)

a/ Đặt x² + 4x + 8 = a

Thì đa thức ban đầu thành

a² + 3ax + 2x² = (a² + 2ax + x²) + (ax + x²)

= (a + x)² + x(a + x) = (a + x)(a + 2x)

b)=4a²-8ab+4b²-a²-2ab-b²

=3a²-6ab+3b²

=3(a²-2ab+b²)

=3(a-b)²

c, 4 - y^2 - x^2 + 2xy

= 4-(x^2 - 2xy + y^2) 

= 4-(x - y)^2 

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

d, x^2 - 2x - 80

= x^2 + 8x - 10x - 80

= x(x + 8) - 10(x + 8)

= (x - 10(x + 8)