Question

Phân tích đa thức thành nhân tử :

1) x​⁴ - x³ -x+1

2) 8xy³ - 5xyz - 24y² + 15z

3) x² - y² + 2x +1 

4) x² +2xz -y² +2ty +z² - t²

5) 2x² - y² +xy

6) y² - y - 12

Giup mik vs tks nhiu

Answer 1

a.

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

b.

\(8xy^3-5xyz-24y^2+15z=8y^2\times\left(xy-3\right)-5z\left(xy-3\right)=\left(xy-3\right)\left(8y^2-5z\right)\)

c.

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

d.

\(x^2+2xz-y^2+2ty+z^2-t^2=\left(x+z\right)^2-\left(y-t\right)^2=\left(x+z+y-t\right)\left(x+z-y+t\right)\)

e.

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

f.

\(y^2-y-12=y^2-3y+4y-12=y\times\left(y-3\right)+4\times\left(y-3\right)=\left(y-3\right)\left(y+4\right)\)

Answer 2

\(x^4-x^3-x+1\)

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

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

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

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