Question

Phân tích các đa thức sau thành nhân tử:

x⁴ + x³ + 2x² + x + 1

4x² - 4x - 3

4x⁴ + 81

x² - 6xy - 25 + 9y²

x² - 8y² - 2xy

Giải chi tiết giùm mik nha, thank you!!

Answer 1

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

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

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

c)  \(4x^4+81=4x^4+36x^2+81-36x^2\)

\(=\left(2x^2+9\right)^2-36x^2=\left(2x^2-6x+9\right)\left(2x^2+6x-9\right)\)

d)  \(x^2-6xy-25+9y^2=\left(x-3y\right)^2-25=\left(x-3y-5\right)\left(x-3y+5\right)\)

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