Question

Viết đa thức sau dưới dạng tích

x\(^3\)+6x\(^2\)+11x+6

Answer 1

x³+6x²+11x+6=x³+6x²+9x+2x+6

=x.(x²+6x+9)+2.(x+3)

=x.(x²+3x+3x+9)+2.(x+3)

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

=x.(x+3)(x+3)+2.(x+3)

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

=(x+3)(x²+3x+2)

=(x+3)(x²+x+2x+2)

=(x+3)[x.(x+1)+2.(x+1)]

=(x+1)(x+2)(x+3)

Answer 2

x³ + 6x² + 11x + 6 = (x³ + x²) + (5x² + 5x) + (6x + 6) = x²(x + 1) + 5x(x + 1) + 6(x+1) = (x+1)(x² + 5x + 6) = (x+1)(x² + 2x + 3x + 6) = (x+1)[x(x+2) + 3(x+2)] = (x+1)(x+2)(x+3)