Question

phân tích đa thức

x^4+6x^3+11x^2+6x+1

x^4+x^3+x^2+x+1

6x^4+5x^3-38x^2+5x+6

x^4+5x^3-12x^2+5x+1

Answer 1

help me

Answer 2

a)\(x^4+6x^3+11x^2+6x+1\)

\(=x^4+9x^2+1+6x^3+6x+2x^2\)

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

Answer 3

\(x^4+5x^3-12x^2+5x+1\)

\(=\left(x^4-2x^3+x^2\right)+\left(7x^3-14x^2+7x\right)+\left(x^2-2x+1\right)\)

\(=x^2\left(x^2-2x+1\right)+7x\left(x^2-2x+1\right)+\left(x^2-2x+1\right)\)

\(=\left(x^2+7x+1\right)\left(x^2-2x+1\right)\)

\(=\left(x^2+7x+1\right)\left(x-1\right)^2\)

Answer 4

\(6x^4+5x^3-38x^2+5x+6\)

\(=\left(6x^4+6x^3-36x^2\right)-\left(x^3+x^2-6x\right)-\left(x^2+x-6\right)\)

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

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

\(=\left(6x^2-3x+2x-1\right)\left[x\left(x-2\right)+3\left(x-2\right)\right]\)

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

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