a: \(n^3-2⋮n-2\)

=>\(n^3-8+6⋮n-2\)

=>\(6⋮n-2\)

=>\(n-2\in\left\{1;-1;2;-2;3;-3;6;-6\right\}\)

=>\(n\in\left\{3;1;4;0;5;-1;8;-4\right\}\)

b: \(n^3-3n^2-3n-1⋮n^2+n+1\)

=>\(n^3+n^2+n-4n^2-4n-4+3⋮n^2+n+1\)

=>\(3⋮n^2+n+1\)

=>\(n^2+n+1\in\left\{1;-1;3;-3\right\}\)

mà \(n^2+n+1=\left(n+\dfrac{1}{2}\right)^2+\dfrac{3}{4}>=\dfrac{3}{4}\forall n\)

nên \(n^2+n+1\in\left\{1;3\right\}\)

=>\(\left[{}\begin{matrix}n^2+n+1=1\\n^2+n+1=3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}n^2+n=0\\n^2+n-2=0\end{matrix}\right.\)

=>\(\left[{}\begin{matrix}n\left(n+1\right)=0\\\left(n+2\right)\left(n-1\right)=0\end{matrix}\right.\Leftrightarrow n\in\left\{0;-1;-2;1\right\}\)

làm hộ?????

3)

3n+7\(⋮2n+1\)

vì \(3n+7⋮3n+7\)

=>\(2\left(3n+7\right)⋮3n+7\)

=> 6n+7\(⋮3n+7\)

vì \(2n+1⋮2n+1\)

\(\Rightarrow3\left(2n+1\right)⋮2n+1\)

\(\Rightarrow6n+1⋮2n+1\)

\(\Rightarrow\left(6n+7\right)-\left(6n+1\right)⋮2n+1\)

\(\Rightarrow6⋮2n+1\)

đến đoạn này em chỉ cần lập bảng tìm n nữa là xong nhé

tìm n để 3n-2 chia hết cho n+4

ai làm đúng mk k cho

a)  \(n+7⋮n+2\)

=) \(\left[n+7-\left(n+2\right)\right]⋮n+2\)

=) \(n+7-n-2⋮n+2\)

=) \(5⋮n+2\)

=) \(n+2\inƯ\left(5\right)\)= \(\left\{+-1;+-5\right\}\)

=) \(n\in\left\{-3;-1;3;-7\right\}\)

đăng kí kênh V-I-S hộ mình nha !

b) \(9-n⋮n-3\)

=) \(\left[9-n+\left(n-3\right)\right]⋮n-3\)

=) \(9-n+n-3\)\(⋮n-3\)

=) \(6⋮n-3\)

=) \(n-3\inƯ\left(6\right)=\left\{+-1;+-2;+-3;+-6\right\}\)

=) \(n\in\left\{2;4;5;1;0;6;9;-3\right\}\)

ta có : n+7 chia hết n+2

=> (n+2)+5 chia hết cho n+2

=> 5 chia hết n+2

=> n+2 c Ư (5) = { 1;5 }

+) n+2 = 1 => n=-1

+) n+2=5 => n=3

vậy n = -1 và n = 3

Ta có:

\(n+7⋮n+2\)

\(\Leftrightarrow\left(n+2\right)+5⋮n+2\)

Vì \(n+2⋮n+2\)

Để \(\left(n+2\right)+5⋮n+2\)

Thì \(5⋮n+2\)

\(\Rightarrow n+2\inƯ\left(5\right)=\left\{1;5\right\}\)

\(\Rightarrow\orbr{\begin{cases}n+2=1\\n+2=5\end{cases}\Rightarrow\orbr{\begin{cases}n=-1\\n=3\end{cases}}}\)

Vậy....

3,\(n^2+n+17⋮n+1\)

\(=>n.\left(n+1\right)+17⋮n+1\)

Do \(n.\left(n+1\right)⋮n+1\)

\(=>17⋮n+1\)

\(=>n+1\inƯ\left(17\right)\)

\(=>n+1\in\left\{-17;-1;1;17\right\}\)

\(=>n\in\left\{-18;-2;0;16\right\}\)

1) Để \(3n+7⋮2n+1\) \(\Leftrightarrow\)\(2.\left(3n+7\right)⋮2n+1\)

- Ta có: \(2.\left(3n+7\right)=6n+14=\left(6n+3\right)+11=3.\left(2n+1\right)+11\)

-  Để \(2.\left(3n+7\right)⋮2n+1\)\(\Rightarrow\)\(3.\left(2n+1\right)+11⋮2n+1\)mà \(3.\left(2n+1\right)⋮2n+1\)

\(\Rightarrow\)\(11⋮2n+1\)\(\Rightarrow\)\(2n+1\inƯ\left(11\right)\in\left\{\pm1;\pm11\right\}\)

- Ta có bảng giá trị:

Vậy \(n\in\left\{-6,-1,0,5\right\}\)

2) Ta có: \(n^2+25=\left(n^2-4\right)+29=\left(n+2\right).\left(n-2\right)+29\)

- Để \(n^2+25⋮n+2\)\(\Rightarrow\)\(\left(n+2\right).\left(n-2\right)+29⋮n+2\)mà \(\left(n+2\right).\left(n-2\right)⋮n+2\)

\(\Rightarrow\)\(29⋮n+2\)\(\Rightarrow n+2\inƯ\left(29\right)\in\left\{\pm1;\pm29\right\}\)

- Ta có bảng giá trị: 

 Vậy \(n\in\left\{-31,-3,-1,27\right\}\)

3) Ta có: \(3n^2+5=\left(3n^2-3\right)+8=3.\left(n+1\right).\left(n-1\right)+8\)

- Để \(3n^2+5⋮n-1\)\(\Rightarrow\)\(3.\left(n+1\right).\left(n-1\right)+8⋮n-1\)mà \(3.\left(n+1\right).\left(n-1\right)⋮n-1\)

\(\Rightarrow\)\(8⋮n-1\)\(\Rightarrow n-1\inƯ\left(8\right)\in\left\{\pm1;\pm2;\pm4;\pm8\right\}\)

- Ta có bảng giá trị:

Vậy \(n\in\left\{-7,-3,-1,0,2,3,5,9\right\}\)