Question

Phân tích đa thức thành nhân tử:

a) 3x² + 9x - 30

b) x² - 9x + 18

c) x² - 7x + 12

d) x² + 4xy - 21y²

e) 5x² + 6xy + y²

f) x² + 2xy - 15y²

g) x² - 7xy + 10y²

h) 4x⁴ + 1

i) x⁴ + 324

Answer 1

a) 3x² +9x - 30

= 3(x² + 3x -10) = 3[(x² -2x)+(5x-10)]

= 3(x-2)(x+5)

b) x² -9x + 18 = (x² - 3x) - (6x-18)

= (x-3)(x-6)

c) x² -7x +12 = (x² -3x)-(4x-12)

= (x-3)(x-4)

d) x² + 4xy -21y² = (x² -3xy)+(7xy - 21y²)

= (x-3y)(x+7y)

e) 5x² + 6xy +y²

= (5x² + 5xy)+(xy+y²)

= (x+y)(5x+y)

f) x² +2xy-15y² = (x² - 3xy)+(5xy-15y²)

= (x-3y)(x+5y)

g) x² -7xy+10y² = (x² - 2xy)-(5xy-10y²)

= (x-2y)(x-5y)

h) 4x⁴ +1 = [(2x²)² + 4x² + 1 ] - 4x²

= (2x² +1)² -(2x)²

= (2x² + 1-2x)(2x² +1+2x)

i) x⁴ + 324 = [x⁴ + 36x² + 18²] - 36x²

= (x² + 18)² - (6x)²

= (x² -6x +18)(x² +6x+18)

Answer 2

3x²+9x-30

=3(x2+3x-10)

=3(x2+5x-2x-10)

=3[(x2+5x)-(2x+10)]

=3[x(x+5)+2(x+5)]

=3(x+5)(x+2)

Answer 3