Phân tích đa thức x^2 - 9+ (x-3) thành nhân tử

a ) \(x^2-9+\left(x-3\right)\)

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

\(=\left(x-3\right)\left(x+3+1\right)\)

\(=\left(x-3\right)\left(x+4\right)\)

b ) \(x^3-4x^2+4x-xy^2\)

\(=x\left(x^2-4x+4-y^2\right)\)

\(=x\left[\left(x-2\right)^2-y^2\right]\)

\(=x\left(x-2-y\right)\left(x-2+y\right)\)

c ) \(x^3-4x^2+12x-27\)

\(=\left(x^3-27\right)-\left(4x^2-12x\right)\)

\(=\left(x-3\right)\left(x^2+3x+9\right)-4x\left(x-3\right)\)

\(=\left(x-3\right)\left(x^2+3x+9-4x\right)\)

\(=\left(x-3\right)\left(x^2-x+9\right)\)

d ) \(3x^2-7x-10\)

\(=3x^2+3x-10x-10\)

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

\(=3x\left(x+1\right)-10\left(x+1\right)\)

\(=\left(x+1\right)\left(3x-10\right)\)

e ) \(5x^3-5x^2y-10x^2+10xy\)

\(=\left(5x^3-5x^2y\right)-\left(10x^2-10xy\right)\)

\(=5x^2\left(x-y\right)-10x\left(x-y\right)\)

\(=\left(x-y\right)\left(5x^2-10x\right)\)

\(=5x\left(x-y\right)\left(x-2\right)\)

f ) \(3x^3-6xy+3y^2-12z^2\)

\(=3\left(x-2xy+y^2-4z^2\right)\)

\(=3\left[\left(x-y\right)^2-\left(2z\right)^2\right]\)

\(=3\left(x-y-2z\right)\left(x-y+2z\right)\)

Phân tích các đa thức sau thành nhân tử:

a) \(x^4+2x^2-3\)

b) \(\left(x^2+2x\right).\left(x^2+2x+4\right)+3\)

c) \(2xy^2+4xy+2x-2xz^2+4xzt-2xt^2\)

Làm hộ mik nha mik đang cần gấp mai phải nộp rồi!

a) \(15xy-20x^2=5.\left(3xy-4x^2\right)\)

b) \(\left(x-4\right)^2-\left(y-5\right)^2\)

= \(\left(x-4-y+5\right).\left(x-4+y-5\right)\)

= \(\left(x-y+1\right).\left(x+y-9\right)\)

c) \(x^4-9x^3-x^2+9x\)

= \(x^3.\left(x-9\right)-x.\left(x-9\right)\)

= \(\left(x-9\right).\left(x^3-x\right)=\left(x-9\right).x.\left(x^2-1\right)\)

= \(\left(x-9\right).x.\left(x-1\right).\left(x+1\right)\)

d) \(2x^2-7x+5\)

= \(2x^2-2x-5x+5\)

= \(2x.\left(x-1\right)-5.\left(x-1\right)\)

= \(\left(x-1\right).\left(2x-5\right)\)

e) \(\left(x+1\right)\left(x+3\right)\left(x+5\right)\left(x+7\right)+15\)

= \(\left(x^2+8x+7\right).\left(x^2+8x+15\right)+15\) (*)

ĐẶT \(x^2+8x+7\) = a

Phương trình (*) \(\Leftrightarrow a\left(a+8\right)+15\)

= \(a^2+8a+15\)

= \(\left(a+3\right)\left(a+5\right)\)

\(=\left(x^2+8x+7+3\right)\left(x^2+8x+7+5\right)\)

= \(\left(x^2+8x+10\right)\left(x^2+8x+12\right)\)

= \(\left(x^2+8x+10\right)\left(x+2\right)\left(x+6\right)\)

a, \(9x^2+6xy+y^2=9x^2+3xy+3xy+y^2\)

\(=\left(9x^2+3xy\right)+\left(3xy+y^2\right)\)

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

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

b, \(x^4+2x^3+x^2=x^4+x^3+x^3+x^2\)

\(=\left(x^4+x^3\right)+\left(x^3+x^2\right)\)

\(=x^3.\left(x+1\right)+x^2.\left(x+1\right)\)

\(=\left(x+1\right).\left(x^3+x^2\right)=\left(x+1\right).x^2.\left(x+1\right)\)

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

Chúc bạn học tốt!!!

a, \(x^4+2x^2-3\)\(=\left[\left(x^2\right)^2+2.x^2.1+1\right]-\left(1-3\right)\)

\(=\left(x^2+1\right)^2-\left(\sqrt{2}\right)^2\)

\(=\left(x^2+1-\sqrt{1}\right)\left(x^2+1+\sqrt{2}\right)\)

b,\(\left(x^2+2x\right)\left(x^2+2x+4\right)+3=x^4+2x^3+4x^2+2x^3+4x^2+8x\)

\(=\left(x^4+4x^3\right)+\left(8x^2+8x\right)=x\left(x^3+4x^2\right)+x\left(8x+8\right)\)

\(=x\left(x^3+4x^2+8x+8\right)\)

c,\(2xy^2+4xy+2x-2xz^2+4xzt-2xt^2\)

\(=\left(2xy^2+4xy\right)+\left(2x-2xz^2\right)+\left(4xzt-2xt^2\right)\)

\(=2x\left(y^2+2y\right)+2x\left(1-z^2\right)+2x\left(2zt-t^2\right)\)

\(=2x\left(y^2+2y+1-z^2+2zt-t^2\right)\)

\(=2x\left[\left(y^2+2y+1\right)-\left(z^2-2zt+t^2\right)\right]\)

\(=2x\left[\left(y+1\right)^2-\left(z-t\right)^2+\left(2y-t^2\right)\right]\)

\(=2x\left[\left(y+1-z-t\right)\left(y+1+z-t\right)\right]\)

Phần a thành nhân tử sẵn rồi bạn:)

b,\(x^6-9x^3+8=x^6-x^3-8x^3+8\)

\(=x^3\left(x^3-1\right)-8\left(x^2-1\right)\)

\(=x^3\left(x-1\right)\left(x^2+x+1\right)-8\left(x-1\right)\left(x+1\right)\)

\(=\left(x-1\right)\left(x^4-x^3-8x-1\right)\)

a)

\(x^3-19x-30\\ =x^3-25x+6x-30\\ =x\left(x^2-5\right)+6\left(x-5\right)\\ =x\left(x+5\right)\left(x-5\right)+6\left(x-5\right)\\ =\left(x-5\right)\left(x^2+5x-6\right)\\ =\left(x-5\right)\left(x-1\right)\left(x+6\right)\)

b)TT

1. Phân tích đa thức thành nhân tử

\(a,x^3\left(2x^2-4x+1\right)\)

\(b,x^6-9x^3+8\)

\(c,2x^3-35x+75\)

\(d,4x^3+6x^2+4x+1\)

2.Tính S=\(\dfrac{3^3+1^3}{2^3-1^3}+\dfrac{5^3+2^3}{3^3-2^3}+\dfrac{7^3+3^3}{4^3-3^3}+...+\dfrac{4009^3+2004^3}{2005^3-2004^3}\)

Phân tích đa thức thành nhân tử

a, \(15xy-20x^2\)

b, \(\left(x-4\right)^2-\left(y-5\right)^2\)

c, \(x^4-9x^3-x^2+9x\)

d, \(2x^2-7x+5\)

e, ( x+1) (x+3) (x+5) (x+7) +15

f, 4x⁸ +1

Bài 3: phân tích đa thức thành nhân tử:

a) 9x^2 + 6xy +y^2

b) x^4 +2x^3 +x^2

c) 5x^2 - 10xy + 5xy^2 - 5z^2

giúp mik zới *_*!!!

phân tích đa thức thành nhân tử: \(x^3+5x^2+3x+9\)

Phân tích các đa thức thành nhân tử ( tách 1 hạng tử thành nhiều hạng tử)

a,x^3-19x-30

b.x^2-6x+8

phân tích đa thức thành nhân tử: x^5 + x + 1

\(x^3+3x^2+2x^2+6x-3x-9\) Hình như đề sai: phải là -9

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

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

\(x^5+x^4-x^4+x^3-x^3+x^2-x^2+x+1\)

\(=\left(x^5+x^4+x^3\right)-\left(x^4+x^3+x^2\right)+\left(x^2+x+1\right)\)

\(=x^3\left(x^2+x+1\right)-x^2\left(x^2+x+1\right)+\left(x^2+x+1\right)\)

\(=\left(x^3-x^2+1\right)\left(x^2+x+1\right)\)