Question

Phân tích đa thức sau thành nhân tử:

a,x^3-1+5x^2-5+3x-3

b,a^5+a^4+a^3+a^2+a+1 c,ab(x^2+y^2)+xy(a^2+b^2)

Answer 1

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

\(=\left(x-1\right)\left(x^2+x+1\right)+5\left(x^2-1\right)+3\left(x-1\right)\)

\(=\left(x-1\right)\left(x^2+x+1\right)+5\left(x-1\right)\left(x+1\right)+3\left(x-1\right)\)

\(=\left(x-1\right)\left[x^2+x+1+5x+5+3\right]\)

\(=\left(x-1\right)\left(x^2+6x+9\right)\)

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

b, \(a^5+a^4+a^3+a^2+a+1\)

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

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

c, \(ab\left(x^2+y^2\right)+xy\left(a^2+b^2\right)\)

\(=abx^2+aby^2+xya^2+xyb^2\)

\(=ax\left(bx+ay\right)+by\left(ay+bx\right)\)

\(=\left(ax+by\right)\left(ay+bx\right)\)