= 4x⁴ + 625
= ( 2x)² + 25²

= ( 2x^2 -10x + 25) ( 2x^2 + 10x + 25)

\(A=4x^4+625\)

\(=4x^4+100x^2+625-100x^2\)

\(=\left(2x^2+25\right)^2-100x^2\)

\(=\left(2x^2+5x+25\right)\left(2x^2-5x+25\right)\)

\(4x^4-8x^3+4x^3-8x^2+x^2-2x-2x+4\\ =4x^3\left(x-2\right)+4x^2\left(x-2\right)+x\left(x-2\right)-2\left(x-2\right)\\ =\left(x-2\right)\left(4x^3+4x^2+x-2\right)\\ =\left(x-2\right)\left(4x^3-2x^2+6x^2-3x+4x-2\right)\\ =\left(x-2\right)\left[2x^2\left(2x-1\right)+3x\left(2x-1\right)+2\left(2x-1\right)\right]\\ =\left(x-2\right)\left(2x-1\right)\left(2x^2+3x-2\right)\)

\(1,=x\left(x^2-2x+1-y^2\right)=x\left[\left(x-1\right)^2-y^2\right]=x\left(x-y-1\right)\left(x+y-1\right)\\ 2,=\left(x+y\right)^3\\ 3,=\left(2y-z\right)\left(4x+7y\right)\\ 4,=\left(x+2\right)^2\\ 5,Sửa:x\left(x-2\right)-x+2=0\\ \Leftrightarrow\left(x-2\right)\left(x-1\right)=0\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)

Đề sai.

#)Giải :

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

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

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

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

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

\(x^4+2x^3+5x^2+4x-12\)

\(=x^4+x^3+6x^2+x^3+x^2+6x-2x^2-2x-12\)

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

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

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

Câu 1.

Đoán được nghiệm là 2.Ta giải như sau:

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

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

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

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

cảm ơn nha!

1.A

2.C

3.B

4.C

a

c

b

c

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

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