Question

Phân tích đa thức thành nhân tử:

a) 3 (x⁴ + x² + 1) - (x² + x + 1)²

b) 4x⁴ + 4x³ + 5x² + 2x + 1

c) x⁸ + x + 1

d) x⁸ + 3x⁴ + 1

e)x⁴ - 8x + 63

Answer 1

b/ 4x⁴ + 4x³ + 5x² + 2x + 1

= (4x⁴ + 4x³ + x²) + 2(2x² + x) + 1

= (2x² + x)² + 2(2x² + x) + 1

= (2x² + x + 1)²

c/  x⁸ + x + 1 = (x² + x + 1)(x⁶ - x⁵ + x³ - x² + 1)

e/ x⁴ - 8x + 63 = (x² - 4x + 7)(x² + 4x + 9)

Answer 2

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

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

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

Answer 3

\(x^8+x+1\)

\(=x^8+x^7+x^6-x^7-x^6-x^5+x^5+x^4+x^3-x^4-x^3-x^2+x^2+x+1\)

\(=x^6\left(x^2+x+1\right)-x^5\left(x^2+x+1\right)+x^3\left(x^2+x+1\right)-x^2\left(x^2+x+1\right)+\left(x^2+x+1\right)\)

\(=\left(x^2+x+1\right)\left(x^6-x^5+x^3-x^2+1\right)\)