Question

phân tích các đa thức sau thành nhân tử

a) 6x²y - 3y² - 2x² + y

b) 2x² +x - 4xy -2y +2x +1

c) 16x²y - 4xy² - 4x³ + x²y

d) 4x² - 20x + 25 - 36y²

e) x² - 4y² + 6x - 4y + 8

g) x¹⁰ + x⁵ +1

h) x⁸ +x +1

Answer 1

Ta có:

a) 6x²y - 3y² - 2x² + y = (6x²y - 2x²) - (3y² - y) = 2x²(3y - 1) - y(3y - 1) = (2x² - y)(3y - 1)

b)  2x² + x - 4xy - 2y + 2x + 1 = (x² + x) - (4xy + 2y) + (x² + 2x + 1) = x(x + 1) - 2y(2x + 1) + (x + 1)²

 = (x + x + 1)(x + 1) - 2y(2x + 1) = (2x + 1)(x + 1) - 2y(2x + 1) = (2x + 1)(x + 1 - 2y)

c) 16x²y - 4xy² - 4x³ + x²y = 4xy(4x - y) - x²(4x - y) = (4xy - x²)(4x - y)

d) 4x² - 20x + 25 - 36y² = (2x  - 5)² - (6y)² = (2x - 5 - 6y)(2x  - 5 + 6y)

e) x² - 4y² + 6x - 4y + 8 = (x² + 6x + 9) - (4y² + 4y + 1) = (x + 3)² - (2y + 1)² = (x + 3 - 2y - 1)(x + 3 + 2y + 1) = (x + 2 - 2y)(x + 4 + 2y)

Answer 2

g) Ta có : x¹⁰ + x⁵ + 1

= (x¹⁰ - x) + (x⁵ - x²) + (x² + x + 1)

= x(x⁹ - 1) + x²(x³ - 1) + (x² + x + 1)

= x(x³ - 1)(x⁶ + x³ + 1) + x²(x³ - 1) + (x² + x + 1)

= (x⁷ + x⁴ + x)(x - 1)(x² + x + 1) + x²(x - 1)(x² + x + 1) + (x² + x + 1)

= (x² + x + 1)(x⁸ - x⁷ + x ⁵ - x⁴ + x² - x + x⁴ + x³ + x² + 1)

= (x² + x + 1)(x⁸ - x⁷ + x⁵ + x³ - x + 1)

h) TT trên (dài dòng ktl)