Phân tích đa thức thành nhân tử:
a) 3x2 - 5x - 8
b) x4 + 6x3 + 9x2 - 16
Phân tích đa thức thành nhân tử:
a)4x3y2-8x2y+12xy2
b)3x2-6xy-5x+10y
c)x2-49+4y2-4xy
d)x2-6x-16
a) \(4x^3y^2-8x^2y+12xy^2=4xy\left(x^2y-2x+3y\right)\)
b) \(3x^2-6xy-5x+10y=3x\left(x-2y\right)-5\left(x-2y\right)=\left(x-2y\right)\left(3x-5\right)\)
c) \(x^2-49+4y^2-4xy=\left(x-2y\right)^2-49=\left(x-2y-7\right)\left(x-2y+7\right)\)
d) \(x^2-6x-16=\left(x^2-6x+9\right)-25=\left(x-3\right)^2-25=\left(x-3-5\right)\left(x-3+5\right)=\left(x-8\right)\left(x+2\right)\)
a) 4x3y2−8x2y+12xy2=4xy(x2y−2x+3y)4x3y2−8x2y+12xy2=4xy(x2y−2x+3y)
b) 3x2−6xy−5x+10y=3x(x−2y)−5(x−2y)=(x−2y)(3x−5)3x2−6xy−5x+10y=3x(x−2y)−5(x−2y)=(x−2y)(3x−5)
c) x2−49+4y2−4xy=(x−2y)2−49=(x−2y−7)(x−2y+7)x2−49+4y2−4xy=(x−2y)2−49=(x−2y−7)(x−2y+7)
d) x2−6x−16=(x2−6x+9)−25=(x−3)2−25=(x−3−5)(x−3+5)=(x−8)(x+2)
Phân tích đa thức thành nhân tử:
a)4x3y2-8x2y+12xy2
b)3x2-6xy-5x+10y
c)x2-49+4y2-4xy
d)x2-6x-16
a) \(4x^3y^2-8x^2y+12xy^2=4xy.x^2y-4xy.2x+4xy.3y=4xy\left(x^2y-2x+3y\right)\)
b) \(3x^2-6xy-5x+10y=\left(3x^2-6xy\right)-\left(5x-10y\right)=3x\left(x-2y\right)-5\left(x-2y\right)=\left(x-2y\right)\left(3x-5\right)\)
c) \(x^2-49+4y^2-4xy=\left(x^2-4xy+4y^2\right)-49=\left(x-2y\right)^2-7^2=\left(x-2y-7\right)\left(x-2y+7\right)\)
d) \(x^2-6x-16=\left(x^2-8x\right)+\left(2x-16\right)=x\left(x-8\right)+2\left(x-8\right)=\left(x-8\right)\left(x+2\right)\)
Phân tích các đa thức sau thành nhân tử:
a) x2 + 5x + 4
b) 3x2 + 4x - 7
c) x2 + 7x + 12
a) \(x^2+5x+4==x\left(x+1\right)+4\left(x+1\right)=\left(x+1\right)\left(x+4\right)\)
b) \(3x^2+4x-7=3x\left(x-1\right)+7\left(x-1\right)=\left(x-1\right)\left(3x+7\right)\)
c) \(x^2+7x+12=x\left(x+3\right)+4\left(x+3\right)=\left(x+3\right)\left(x+4\right)\)
a) x2+5x+4 = x(x+4)+(x+4) = (x+4)(x+1)
b) 3x2+4x-7 = 3x(x-1)+7(x-1) = (x-1)(3x+7)
c) x2+7x+12 = x(x+4)+3(x+4) = (x+3)(x+4)
Phân tích đa thức thành nhân tử:
a,x2 + xy + 5x + 5y
b,xy - x2 - 3y + 3x
c,2x3 - 6x3 + 18x
d, x2 - 4x - 4y2 + 4
e, x2 - 10x + 9
f, 4x2 - 4x - 3
\(a,=x\left(x+y\right)+5\left(x+y\right)=\left(x+5\right)\left(x+y\right)\\ b,=x\left(y-x\right)-3\left(y-x\right)=\left(x-3\right)\left(y-x\right)\\ c,=18x-4x^3=2x\left(9-2x^2\right)\\ d,=\left(x-2\right)^2-4y^2=\left(x-2y-2\right)\left(x+2y-2\right)\\ e,=x^2-x-9x+9=\left(x-1\right)\left(x-9\right)\\ f,=4x^2-6x+2x-3=\left(2x-3\right)\left(2x+1\right)\)
phân tích đa thức thành nhân tử :
a.9x2-3x+2y-4y2
b.3x2-6xy+3y2-5x+5y
a)
\(9x^2-3x+2y-4y^2\\=(9x^2-4y^2)-(3x-2y)\\=[(3x)^2-(2y)^2]-(3x-2y)\\=(3x-2y)(3x+2y)-(3x-2y)\\=(3x-2y)(3x+2y-1)\)
b)
\(3x^2-6xy+3y^2-5x+5y\\=3(x^2-2xy+y^2)-5(x-y)\\=3(x-y)^2-5(x-y)\\=(x-y)[3(x-y)-5]\\=(x-y)(3x-3y-5)\\Toru\)
Phân tích các đa thức sau thành nhân tử:
a/ y2 - 2y b/ 3x4 – 6x3 + 3x2
c/ 27x2 ( y – 1) – 9x3 ( 1 - y) d/y3 – 2y2 + y
e/ x3 + 6x2 + 9x f/ x3 – 2x2y + xy2
g/ x( 2- x) – x + 2 h/ 3x ( x – 1) + 6( 1 – x)
\(a,=y\left(y-2\right)\\ b,=3x\left(x^2-2x+1\right)=3x\left(x-1\right)^2\\ c,=\left(y-1\right)\left(27x^2+9x^3\right)=9x^2\left(x+3\right)\left(y-1\right)\\ d,=y\left(y^2-2y+1\right)=y\left(y-1\right)^2\\ e,=x\left(x^2+6x+9\right)=x\left(x+3\right)^2\\ f,=x\left(x^2-2xy+y^2\right)=x\left(x-y\right)^2\\ g,=\left(2-x\right)\left(x+1\right)\\ h,=\left(x-1\right)\left(3x-6\right)=3\left(x-1\right)\left(x-2\right)\)
a: =y(y-2)
b: \(=3x^2\left(x^2-2x+1\right)=3x^2\left(x-1\right)^2\)
d: \(=y\left(y^2-2y+1\right)=y\left(y-1\right)^2\)
Phân tích đa thức sau thành nhân tử:
a) 14x2y - 21xy2 + 28x2y2
b) 3x2- 5x - 3xy + 5y
c) 5a3 - 20a
d) 2x+ 2y + x2+ 2xy + y2
a) \(14x^2y-21xy^2+28x^2y^2\)
\(=7xy\left(2x-3y+4xy\right)\)
b) \(3x^2-5x-3xy+5y\)
\(=\left(3x^2-3xy\right)-\left(5x-5y\right)\)
\(=3x\left(x-y\right)-5\left(x-y\right)\)
\(=\left(x-y\right)\left(3x-5\right)\)
c) \(5a^3-20a\)
\(=5a\left(a^2-4\right)\)
\(=5a\left(a-2\right)\left(a+2\right)\)
d) \(2x+2y+x^2+2xy+y^2\)
\(=2\left(x+y\right)\left(x+y\right)^2\)
= \(=\left(x+y\right)\left(2+x+y\right)\)
Phân tích đa thức thành nhân tử:
a) x 4 - 6 x 3 + 12 x 2 - 14x + 3.
b) x 4 + 6 x 3 + 7 x 2 -6x + l.
a) ( x 2 – 4x + 1)( x 2 – 2x + 3).
b) ( x 2 + 5x – 1)( x 2 + x – 1).
Phân tích đa thức thành nhân tử:
a)9x2-y2+6x+1
b)x3-5x2+6x
\(a,=\left(3x+1\right)^2-y^2=\left(3x-y+1\right)\left(3x+y+1\right)\\ b,=x\left(x^2-5x+6\right)=x\left(x^2-2x-3x+6\right)=x\left(x-2\right)\left(x-3\right)\)
Phân tích đa thức thành nhân tử:
a.10x2y – 20xy2 b. x2 – y2 + 10y – 25 c. x2 – y2 + 3x – 3y
d. x3 + 3x2 – 16x – 48 e. 9x3 + 6x2 + x f. x4 + 5x3 + 15x – 9
\(a,10x^2y-20xy^2=10xy\left(x-2y\right)\\ b,x^2-y^2+10y-25=x^2-\left(y^2-10y+25\right)=x^2-\left(y-5\right)^2=\left(x-y+5\right)\left(x+y-5\right)\\ c,x^2-y^2+3x-3y=\left(x-y\right)\left(x+y\right)+3\left(x-y\right)=\left(x-y\right)\left(x+y+3\right)\\ d,x^3+3x^2-16x-48=\left(x^3+3x^2\right)-\left(16x+48\right)=x^2\left(x+3\right)-16\left(x+3\right)=\left(x+3\right)\left(x^2-16\right)=\left(x+3\right)\left(x+4\right)\left(x-4\right)\)
\(e,9x^3+6x^2+x=x\left(9x^2+6x+1\right)=x\left(3x+1\right)^2\\ f,x^4+5x^3+15x-9=\left(x^4+5x^3-3x^2\right)+\left(3x^2+15x-9\right)=x^2\left(x^2+5x-3\right)+3\left(x^2+5x-3\right)=\left(x^2+3\right)\left(x^2+5x-3\right)\)