Phân tích đa thức thành nhân tử

1. x⁵ + x + 1

2. x⁵ + x⁴ +1

3. 2a²b+4ab²-a²c+ac²-4b²c+2bc-4abc

4. y(x-2z)²+ 8xyz +x(y-2z)²-2z(x+y)²

5. (x²+x)²-2(x²+x)-15

Read the passage and do the tasks below:

Lily is twelve years old. She is in grade six, class 6A1. She lives in a house with her mother, father and sister. Their house is next to a bookstore. In the neighborhood, there is a hospital, a market and a stadium. Lily's father is a doctor. He works in the hospital. Her mother works in the supermarket. Lily goes to school at six- thirty in the morning. She has classes from seven to eleven thirty.

Is their house next to a hospital?

x⁴ + 4 = x⁴ + 4x² + 4 - 4x² = (x⁴ + 4x² + 4) - 4x²

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

Program tamgiac;
Uses crt;
Var
a,b,c:Real;
Begin
Clrscr;
Write('Nhap a ');Readln(a);
Write('Nhap b ');Readln(b);
Write('Nhap c ');Readln(c);
If (a=b)and(b=c) then
Writeln('Ba canh tam giac deu')
Else
Writeln('Ba canh khong phai la ba canh tam giac deu');
Readln;
End.

C

A, C

a) 3x³-12x=0

3x(x²-4)=0

3x(x-2)(x+2)=0

\(\Rightarrow\left[{}\begin{matrix}3x=0\\x-2=0\\x+2=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=2\\x=-2\end{matrix}\right.\)

Vậy x=0,2 hoặc -2

b)2x²-x-6=0

2x²+3x-4x-6=0

(2x²+3x)-(4x+6)=0

x(2x+3)-2(2x+3)=0

(2x+3)(x-2)=0

\(\Rightarrow\left[{}\begin{matrix}2x+3=0\\x-2=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}2x=-3\\x=2\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{-3}{2}\\x=2\end{matrix}\right.\)

Vậy x =-3/2 hoặc 2

(x+2)(x²-4x+4)= x³-4x²+4x+2x²-8x+8

= x³-2x²-8x+8