Phân tích các đa thức sau thành nhân tử:
a) \(3x^2-8x+4\)
b) \(4x^2-4x-3\)
c) \(x^3-x^2-4\)
d) \(4x^4+81\)
e) \(x^5+x-1\)
Phân tích đa thức thành nhân tử:
a) x^3 - x^2 + 8x - 8
b) 8x^3 - 8x^2y + 2xy^2
c) (x^2 + y^2 - z^2)^2 - 4x^2y^2
d) (x^2 - y^2 - 5)^2 - 4(x^2y^2 + 4xy + 4)
e) x^3 - y^3 - 3x^2 + 3x - 1
a) (x3-x2)+(8x-8)=x(x-1)+8(x-1)=(x2+8)(x-1)
b) 8x3-8x2y+2xy2=2x(4x2-4xy+y2)
c) (x2+y2-z2)2 - 4x2y2=(x2+y2-z2)2 - (2xy)2=(x2+y2-z2-2xy)(x2+y2-z2+2xy)
Phân tích đa thức thành nhân tử:
a, \(x^3+3x^2+3x+1-27z^3\)
b, \(x^2-2xy+y^2-xz+yz\)
c, \(x^4+4x^2-5\)
a.
\(=\left(x+1\right)^3-\left(3z\right)^3\)
\(=\left(x+1+3z\right)\left[\left(x+1\right)^2+3z\left(x+1\right)+9z^2\right]\)
\(=\left(x+3z+1\right)\left(x^2+2x+1+3zx+3z+9z^2\right)\)
b.
\(=\left(x-y\right)^2-z\left(x-y\right)\)
\(=\left(x-y\right)\left(x-y-z\right)\)
c.
\(=x^4-1+4x^2-4\)
\(=\left(x^2-1\right)\left(x^2+1\right)+4\left(x^2-1\right)\)
\(=\left(x^2-1\right)\left(x^2+5\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(x^2+5\right)\)
a) Ta có: \(x^3+3x^2+3x+1-27z^3\)
\(=\left(x+1\right)^3-\left(3z\right)^3\)
\(=\left(x+1-3z\right)\left(x^2+2x+1+3xz+3z+9z^2\right)\)
b) Ta có: \(x^2-2xy+y^2-zx+yz\)
\(=\left(x-y\right)^2-z\left(x-y\right)\)
\(=\left(x-y\right)\left(x-y-z\right)\)
c) Ta có: \(x^4+4x^2-5\)
\(=x^4+4x^2+4-9\)
\(=\left(x^2+2\right)^2-3^2\)
\(=\left(x^2-1\right)\left(x^2+5\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(x^2+5\right)\)
Dùng phương pháp đặt biến số phụ, phân tích các đa thức sau thành nhân tử
a. (x^2 + x)^2 - 2(x^2 + x) - 15
b. (x+2)(x+3)(x+4)(x+5) - 24
c. (x^2 + 8x + 7)(x^2 + 8x + 15) + 15
d. (x^2 + 3x + 1)(x^2 + 3x + 2) - 6
e. (4x+1)(12x-1)(3x+2)(x+1) - 4
f. 4(x+5)(x+6)(x+10)(x+12) - 3x^2
g. 3x^6 - 4x^5 + 2x^4 - 8x^3 + 2x^2 - 4x + 3
PHân tích đa thức thành nhân tử
A, x^3 - 4x^2 - 8x + 8
b, 6x^3 - x^2 - 486x + 81
c, x^(x^2 + 4) - x^2 + 4
d, x^4 - x^2 +4x - 1
e, x^(x + 4 ) - ( x + 4)^2 - ( x^2 - 1)
\(x^3-4x^2-8x+8\)
\(=x^3+2x^2-6x^2-12x+4x+8\)
\(=x^2\left(x+2\right)-6x\left(x+2\right)+4\left(x+2\right)\)
\(=\left(x+2\right)\left(x^2-6x+4\right)\)
phân tích đa thức thành nhân tử
a/4x-4y+x^2-2xy+y^2
b/x^4-4x^3-8x^2+8x
c/x^3+x^2-4x-4
d/x^4-x^2+2x-1
e/x^4+x^3+x^2+1
f/x^3-4x^2+4x-1
\(a/\)
\(4x-4y+x^2-2xy+y^2\)
\(=\left(4x-4y\right)+\left(x^2-2xy+y^2\right)\)
\(=4\left(x-y\right)+\left(x-y\right)^2\)
\(=\left(x-y\right)\left(4+x-y\right)\)
\(b/\)
\(x^4-4x^3-8x^2+8x\)
\(=\left(x^4+8x\right)-\left(4x^3+8x^2\right)\)
\(=x\left(x^3+8\right)-4x^2\left(x+2\right)\)
\(=x\left(x+2\right)\left(x^2-2x+4\right)-4x^2\left(x+2\right)\)
\(=x\left(x+2\right)\left(x^2-2x+4-4x\right)\)
\(=x\left(x+2\right)\left(x^2-6x-4\right)\)
\(d/\)
\(x^4-x^2+2x-1\)
\(=x^4-\left(x-1\right)^2\)
\(=\left(x^2+x-1\right)\left(x^2-x+1\right)\)
\(e/\)(Xem lại đề)
\(x^4+x^3+x^2+2x+1\)
\(=\left(x^4+x^3\right)+\left(x^2+2x+1\right)\)
\(=x^3\left(x+1\right)+\left(x+1\right)^2\)
\(=\left(x+1\right)\left(x^3+x+1\right)\)
\(f/\)
\(x^3-4x^2+4x-1\)
\(=x\left(x^2-4x+4\right)-1^2\)
\(=x\left(x-2\right)^2-1\)
\(=[\sqrt{x}\left(x-2\right)]^2-1\)
\(=[\sqrt{x}\left(x-2\right)-1][\sqrt{x}\left(x-2\right)+1]\)
\(c/\)
\(x^3+x^2-4x-4\)
\(=\left(x^3-2x^2\right)+\left(3x^2-6x\right)+\left(2x-4\right)\)
\(=x^2\left(x-2\right)+3x\left(x-2\right)+2\left(x-2\right)\)
\(=\left(x-2\right)\left(x^2+3x+2\right)\)
\(=\left(x-2\right)[\left(x^2+x\right)+\left(2x+2\right)]\)
\(=\left(x-2\right)\left(x+1\right)\left(x+2\right)\)
Phân tích các đa thức sau thành nhân tử:
a) x^2 +4x +4
b)4x^2 - 4x +1
c)c(x+1) - y(x+1)
d)x^3 - 3x^2 +3x - 1 +27y^3
e) 4(x-y) - 25(x+y)^2
\(x^2+4x+4=\left(x+2\right)^2 \)
\(4x^2-4x+1=\left(2x-1\right)^2\)
\(c\left(x+1\right)-y\left(x+1\right)=\left(x+1\right)\left(c-y\right)\)
\(x^3-3x^2+3x-1+27y^3=\left(x-1\right)^3+27y^3=\left(x-1+3y\right)\left(x^2-2x+1-3xy+3y+9y^2\right)\)
Phân tích đa thức thành nhân tử:
a) x^3 + 3x^2- 3x-1
b)x^3 - 3x^2-3x-1
c) (a^2 +b^2+ ab)^2- a^2b^2-c^2a^2-b^2c^2
d)x^3 - 4x^2-4x+1
e) x^4 - 4x^3- 8x^2+8x
Giúp mình với nhé!!!
a ) \(x^3+3x^2-3x+1\)
\(=x^3-3x+3x^2-1\)
\(=\left(x-1\right)^3\)
c/ (x + 1)(x + \(\frac{\sqrt{21}-5}{2}\))(x + \(\frac{-\sqrt{21}-5}{2}\))
Phân tích đa thức thành các nhân tử:
a)x^2-(a+b)x+ab
b)7x^3-3xyz-21x^2+9z
c)4x+4y-x^2(x+y)
d)y^2+y-x^2+x
e)4x^2-2x-y^2-y
f)9x^2-25y^2-6x+10y
Phân tích đa thức thành nhân tử
a)(5x-4)(4x-5)-(x-3)(x-2)-(5x-4)(3x-2)
b)(5x-4)(4x-5)+(5x-1)(x+4)+3(3x-2)(4-5x)
c)(5x-4)^2+(16-25x^2)+(5x-4)(3x+2)
d)x^4-x^3-x+1
e)x^6-x^4+2x^3+2x^2
a)x^2-(a+b)x+ab
= x^2 - ax - bx + ab
= (x^2 - ax) - (bx - ab)
= x(x-a) - b(x-a)
= (x-b)(x-a)
b)7x^3-3xyz-21x^2+9z
=
c)4x+4y-x^2(x+y)
= 4(x + y) - x^2(x+y)
= (4-x^2) (x+y)
= (2-x)(2+x)(x+y)
d) y^2+y-x^2+x
= (y^2 - x^2) + (x+y)
= (y-x)(y+x)+ (x+y)
= (y-x+1) (x+y)
e)4x^2-2x-y^2-y
= [(2x)^2 - y^2] - (2x +y)
= (2x-y)(2x+y) - (2x+y)
= (2x -y -1)(2x+y)
f)9x^2-25y^2-6x+10y
=
Phân tích đa thức sau thành nhân tử
a) 4x -4y +x^2 -2xy +y^2
b) x^4 -4x^3 -8x^2 +8x
c) x^3 +x^2 -4x -4
d) x^4 -x^2 +2x -1
a 4x -4y +(x-y)^2
=4(x-y)+(x-y).(x-y)
=(x-y).(4+x-y)
c x^2(x+1)-4(x+1)
(x+1).(x^2-4)
d x^4-(x^2-2x+1)
=x^4-(x-1)^2
=x^2(x-x+1)(x-x-1)
MIK KO BIT DUNG HAY KO CON B THI MIK KO BIET LAM
Câu b dễ thôi
\(x^4-4x^3-8x^2+8x\)
\(=x\left(x^3-4x^2-8x+8\right)\)
\(=x\left(x+2\right)\left(x^2-6x+4\right)\)