Question

Tìm x thuộc z

a, ( x² + 3x +3) ⋮ (x+3)

b, (x² + x + 2) ⋮ ( x+1)

Mong mn giúp đỡ mình! Thank you

Answer 1

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

= \(x\left(x+3\right)+3\)

Để \(x^2+3x+3⋮x+3\)

<=> \(x\left(x+3\right)+3⋮\left(x+3\right)\)

mà \(x\left(x+3\right)⋮x+3\)

<=> \(3⋮x+3\)

<=> \(\left(x+3\right)\inƯ\left(3\right)\)

Ta có bảng:

x+3	1	3	-1	-3
x	-2	0	-4	-6

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

Để \(x^2+x+2⋮x+1\)

<=> \(x\left(x+1\right)+2⋮x+1\)

mà \(x\left(x+1\right)⋮x+1\)

<=> 2\(⋮x+1\)

<=> \(x+1\inƯ\left(2\right)\)

ta có bảng:

x+1	1	2	-1	-2
x	0	1	-2	-3