Question

Phân tích đa thức thành nhân tử tổng hợp

a) x^4 + 4x^2 - 5

b) x^6 - x^4 + 2x^3 + 2x^2

Làm rõ các bước ra cho nó dễ hiểu nhen

Answer 1

\(x^4+4x^2-5\)

\(=\left[\left(x^2\right)^2+2.x^2.2+2^2\right]-9\)

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

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

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

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

Answer 2

a)\(x^4+4x^2-5=x^4-x^2+5x^2-5=x^2\left(x^2-1\right)+5\left(x^2-1\right)=\left(x^2-5\right)\left(x^2-1\right)\)

Answer 3

a)  \(x^4+4x^2-5=\left(x^4+4x^2+4\right)-9=\left(x^2+2\right)^2-9\)

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

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

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

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

\(=\left(x+1\right)\left(x^5-x^4+2x^2\right)\)

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

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

Answer 4

\(a,x^4+4x^2-5\)

\(=x^4-x^2+5x^2-5\)

\(=\left(x^4-x^2\right)+\left(5x^2-5\right)\)

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

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

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