\(P=\left(x+2\right)\left(x+4\right)\left(x+6\right)\left(x+8\right)+2008\)

\(=\left(x+2\right)\left(x+8\right)\left(x+4\right)\left(x+6\right)+2008\)

\(=\left(x^2+10x+16\right)\left(x^2+10x+24\right)+2008\)

Đặt \(x^2+10x+21=t\)

\(\Rightarrow P=\left(t-5\right)\left(t+3\right)+2008=t^2-2t+1993\)

\(\Rightarrow P\) chia \(x^2+10x+21\) dư \(1993\)

Ta có (x+2)(x+4)(x+6)(x+8) + 2008 = (x² +10x+16)(x² +10x +24) +2008

= [(x² +10x +21) -5][(x² +10x + 21) +3] +2008 = (x² +10x +21)² +3(x² +10x +21) - 5(x² +10x +21) - 15 +2008

= (x² +10x +21)² -2(x² +10x +21) + 1993

Vậy dư của phép chia là 1993

Ta có : \(P\left(x\right)=\left(x+2\right)\left(x+4\right)\left(x+6\right)\left(x+8\right)+2008\)

                         = \(\left(x^2+10+16\right)\left(x^2+10x+24\right)+2008\)

            Đặt t bằng \(x^2+1x+21\left(t\ne-3;t\ne-7\right)\) biểu thức \(p\left(x\right)\) được viết lại :
\(P\left(x\right)=\left(t-5\right)\left(t+3\right)+2008=t^2-2t+1993\) 

Do đó khi chia \(t^2-2t+1993\) cho t  có số d là 1993 

Chúc bạn học tốt !!!

Ta có:

\(\left(x+2\right)\left(x+4\right)\left(x+6\right)\left(x+8\right)+2008\)

\(=\left(x^2+10x+16\right)\left(x^2+10x+24\right)+2008\)

Đặt \(x^2+10x+21=t\),ta có:

\(\left(t-5\right)\left(t+3\right)+2008\)

\(=t^2-2t-15+2008\)

\(=\left(x^2+10x+21\right)^2-2\left(x^2+10x+21\right)+1993\) chia \(f\left(x\right)=x^2+10x+21\) dư 1993.

đặt A=\(\left[\left(x+2\right)\left(x+8\right)\right]\left[\left(x+4\right)\left(x+6\right)\right]+2015\)

        =\(\left(x^2+10x+16\right)\left(x^2+10x+24\right)+2015\)

         =\(\left(x^2+10x+21-5\right)\left(x^2+10x+21+3\right)+2015\)

         =\(\left(x^2+10x+21\right)^2-5\left(x^2+10x+21\right)+3\left(x^2+10x+21\right)-15+2015\)

         =\(\left(x^2+10x+21\right)^2-2\left(x^2+10x+21\right)+2000\)

vì \(\left(x^2+10x+21\right)^2⋮x^2+10x+21\);\(-2\left(x^2+10x+21\right)⋮x^2+10x+21\)

SUY RA        A\(:x^2+10x+21,\forall x\inℝ\)dư 2000

                                        đáp số 2000

                                                                               kb với mk nha!!!!

Ta có: 

Đặt A=(x+2)(x+4)(x+6)(x+8)+2012

=(x^2+10x+16)(x^2+10x+24)+2012

Đặt y=x^2+10x+21

A=(y-5)(y+3)+2012

=y^2-2y-15+2012

=y(y-2)+1997

Mà y(y-2) chia hết cho x^2+10x+21 nên số dư là 1997

( x + 2 )( x + 4 )( x + 6 )( x + 8 ) + 2012

= [ ( x + 2 )( x + 8 ) ][ ( x + 4 )( x + 6 ) ]] + 2012

= ( x² + 10x + 16 )( x² + 10x + 24 ) + 2012

Đặt y = x² + 10x + 21

= ( y - 5 )( y + 3 ) + 2012 = y² - 2y + 1997 = ( x² + 10x + 21 )² -2 ( x² + 10x + 21 ) + 1997

=> Dư 2027

à xin lõi nhé dư 1997 lú quá :>

moi hok lop 6

(x+2).(x+4).(x+6).(x+8)=\(\left(x+2\right)\left(x+8\right)\left(x+4\right)\left(x+6\right)=\left(x^2+10x+16\right)\left(x^2+10x+24\right)=\left(x^2+10x+21-5\right)\left(x^2+10x+21+4\right)\)

đặt x^2+10x+21=t đi.

\(\left(t-5\right)\left(t+4\right)=t^2-t-20=\left(x^2+10x+21\right)^2-\left(x^2+10x+21\right)-20\)

nhìn là biết dư -20 rồi nha

24  sao bằng 21+4 dzậy bạn???

Ta có (x+2)(x+4)(x+6)(x+8) + 2008 = (x² +10x+16)(x² +10x +24) +2008

= [(x² +10x +21) -5][(x² +10x + 21) +3] +2008 = (x² +10x +21)² +3(x² +10x +21) - 5(x² +10x +21) - 15 +2008

= (x² +10x +21)² -2(x² +10x +21) + 1993

Vậy dư của phép chia là 1993

Bạn tham khảo tại đây :

Câu hỏi của Vương Thị Uyên Phương - Toán lớp 8 - Học toán với OnlineMath

Có \(\left(x+2\right)\left(x+4\right)\left(x+6\right)\left(x+8\right)+2008\)

\(=\left(x+2\right)\left(x+8\right)\left(x+4\right)\left(x+6\right)+2008\)

\(=\left(x^2+10x+16\right)\left(x^2+10x+24\right)+2008\)

Đặt \(x^2+10x+21=a\)

\(\Rightarrow\) \(\left(a-5\right)\left(a+3\right)+2008\)

\(=a^2-2a-15+2008\)

\(=a\left(a-2\right)+1993\)

\(=\left(x^2+10x+21\right)\left(x^2+10x+19\right)+1993\)

Có \(\left(x^2+10x+21\right)\left(x^2+10x+19\right)⋮\left(x^2+10x+21\right)\) \(\)

\(\Rightarrow\)\(\left(x^2+10x+21\right)\left(x^2+10x+19\right)+1993\div\left(x^2+10x+21\right)\) dư 1993

Ta có: \(\left(x+2\right)\left(x+4\right)\left(x+6\right)\left(x+8\right)+2008\)

\(=\left[\left(x+2\right)\left(x+8\right)\right]\left[\left(x+4\right)\left(x+6\right)\right]+2008\)

\(=\left(x^2+10x+16\right)\left(x^2+10x+24\right)+2008\)(*)

Đặt \(a=x^2+10x+21\)

\(\Rightarrow x^2+10x+16=a-5\)

\(x^2+10x+24=a+3\)

Thay \(x^2+10x+16=a-5;x^2+10x+24=a+3\) vào (*) ta được:

\(\left(a-5\right)\left(a+3\right)+2008\)

\(=a^2-2a-15+2008\)

\(=a\left(a-2\right)+1993\)

Vì \(a\left(a-2\right)⋮1993\Rightarrow a\left(a-2\right)+1993\) chia a dư 1993

hay \(\left(x+2\right)\left(x+4\right)\left(x+6\right)\left(x+8\right)+2008\) chia \(x^2+10x+21\) dư 1993