Question

1:phân tich các đa thức sau thành phân tử

a,x⁵+x³-x²-1

b,x²-3x³-x+3

c,x²-6x+8

d,4x⁴+4x²y²-8y⁴

Answer 1

a)

\(x^5+x^3-x^2-1\)

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

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

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

b)

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

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

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

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

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

c)

\(x^2-6x+8\)

\(=x^2-2.x.3+9-1\)

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

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

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

d)

\(4x^4-4x^2y^2-8y^4\)

\(=\left(2x^2\right)^2-2.\left(2x^2\right)y^2+y^2-9y^4\)

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

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