p/t bằng phương pháp tách hạng tử
4x\(^2\)-4x-3
x\(^2\)-5x-14
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H9
HT.Phong (9A5)
CTVHS
22 tháng 10 2023
a) \(x^3+4x^2-21x\)
\(=x\left(x^2+4x-21\right)\)
\(=x\left(x^2-3x+7x-21\right)\)
\(=x\left[x\left(x-3\right)+7\left(x-3\right)\right]\)
\(=x\left(x-3\right)\left(x+7\right)\)
b) \(5x^3+6x^2+x\)
\(=x\left(5x^2+6x+1\right)\)
\(=x\left(5x^2+5x+x+1\right)\)
\(=x\left[5x\left(x+1\right)+\left(x+1\right)\right]\)
\(=x\left(x+1\right)\left(5x+1\right)\)
c) \(x^3-7x+6\)
\(=x^3+2x^2-3x-2x^2-4x+6\)
\(=x\left(x^2+2x-3\right)-2\left(x^2+2x-3\right)\)
\(=\left(x-2\right)\left(x^2+2x-3\right)\)
\(=\left(x-2\right)\left(x-1\right)\left(x+3\right)\)
d) \(3x^3+2x-5\)
\(=3x^3+3x^2+5x-3x^2-3x-5\)
\(=x\left(3x^2+3x+5\right)-\left(3x^2+3x+5\right)\)
\(=\left(x-1\right)\left(3x^2+3x+5\right)\)
19 tháng 10 2020
a) x2 - 3x + 2 = x2 - x - 2x + 2 = x( x - 1 ) - 2( x - 1 ) = ( x - 1 )( x - 2 )
b) 2x2 - x - 6 = 2x2 - 4x + 3x - 6 = 2x( x - 2 ) + 3( x - 2 ) = ( x - 2 )( 2x + 3 )
c) x2 - 5x - 6 = x2 + x - 6x - 6 = x( x + 1 ) - 6( x + 1 ) = ( x + 1 )( x - 6 )
d) x2 + 8x + 7 = x2 + x + 7x + 7 = x( x + 1 ) + 7( x + 1 ) = ( x + 1 )( x + 7 )
e) 3x2 + 2x - 5 = 3x2 - 3x + 5x - 5 = 3x( x - 1 ) + 5( x - 1 ) = ( x - 1 )( 3x + 5 )
f) 4x2 - 3x - 1 = 4x2 - 4x + x - 1 = 4x( x - 1 ) + ( x - 1 ) = ( x - 1 )( 4x + 1 )
A
19 tháng 10 2020
a \(x^2-3x+2=x^2-x-2x+2=\left(x-1\right)\left(x-2\right)\)
b, \(2x^2-x-6=2x^2-4x+3x-6=\left(x-2\right)\left(2x+3\right)\)
c, \(x^2-5x-6=x^2+x-6x-6=\left(x+1\right)\left(x-6\right)\)
d, \(x^2+8x+7=x^2+x+7x+7=\left(x+1\right)\left(x+7\right)\)
e, \(3x^2+2x-5=3x^2-3x+5x-5=\left(x-1\right)\left(3x+5\right)\)
f, \(4x^2-3x-1=4x^2-4x+x-1=\left(x-1\right)\left(4x+1\right)\)
TD
22 tháng 11 2021
a, x2-5x+6=(x2-2x)-(3x-6)=x(x-2)-3(x-2)=(x-2)(x-3)
b, 3x2+9x-30=(3x2-6x)+(15x-30)=3x(x-2)+15(x-2)=3(x-2)(x+5)
c, x2-3x+2=(x2-x)-(2x-2)=x(x-1)-2(x-1)=(x-1)(x-2)
DT
23 tháng 11 2021
a, x^2-5x+6=x^2-2x-3x+6=(x^2-2x)-(3x-6)=x(x-2)-3(x-2)=(x-3)(x-2)
b, 3x^2+9x-30=3x^2-6x+15x-30=(3x^2-6x)+(15x-30)=3x(x-2)+3(x-2)=(3x+3)(x-2)
c, x^2-3x+2=x^2-x-2x+2=(x^2-x)-(2x-2)=x(x-1)-2(x-1)=(x-2)(x-1)
7 tháng 9 2021
\(3x^2-3xy-5x+5y=3x\left(x-y\right)-5\left(x-y\right)=\left(3x-5\right)\left(x-y\right)\\ x^3-3x^2-4x+12=x^2\left(x-3\right)-4\left(x-3\right)=\left(x-2\right)\left(x+2\right)\left(x-3\right)\\ 45+x^3-5x^2-9x=x^2\left(x-5\right)-9\left(x-5\right)=\left(x-3\right)\left(x+3\right)\left(x-5\right)\)
KN
31 tháng 7 2019
\(2\left(x^2+8x+16\right)-x^2+4=0\)
\(\Leftrightarrow2x^2+16x+32-x^2+4=0\)
\(\Leftrightarrow x^2+16x+36=0\)
\(\Delta=16^2-4.1.36=112>0,\sqrt{\Delta}=\sqrt{11}\)
Vập pt có 2 nghiệm phân biệt
\(x_1=\frac{1+\sqrt{112}}{2}\);\(x_2=\frac{1-\sqrt{112}}{2}\)
KN
31 tháng 7 2019
b) \(x^2\left(x-2\right)+7x=14\)
\(\Leftrightarrow x^3-2x^2+7x=14\)
V: pt bậc ba ko bt giải, ms 2k7
2a) \(4x^2-3x-1\)
\(=4x^2-4x+x-1\)
\(=4x\left(x-1\right)+\left(x-1\right)=\left(4x+1\right)\left(x-1\right)\)
25 tháng 6 2017
(4x + 3)2 - (4x - 3)2 = 5x + 2
16x2 + 2.4x.3 + 9 - (16x2 - 2.4x.3 + 9) = 5x + 2
16x2 + 2.4x.3 + 9 - 16x2 + 2.4x.3 - 9 = 5x + 2
48x = 5x + 2
43x = 2
\(x=\frac{2}{43}\)
23 tháng 11 2017
a. 6x3-x2-486x+81
= 6x3-54x2+53x2-477x-9x+81
= 6x2.(x-9)+53x.(x-9)-9.(x-9)
= (x-9).(6x2+53x-9)
= (x-9)(6x2+54x-x-9)
=(x-9)[6x.(x+9)-(x+9)]=(x-9)(x+9)(6x-1)
b. x3-5x2+3x+9
= x3+x2-6x2-6x+9x+9
=x2.(x+1)-6x.(x+1)+9.(x+1)
=(x+1)(x2-6x+9)=(x+1)(x-3)2
c. x3+3x2+6x+4
= x3+x2+2x2+2x+4x+4
= x2.(x+1)+2x.(x+1)+4.(x+1)
= (x+1)(x2+2x+4)
d.
\(4x^2-4x-3\)
\(=4x^2-4x+1-4\)
\(=\left(2x-1\right)^2-2^2\)
\(=\left(2x-1-2\right)\left(2x-1+2\right)\)
\(=\left(2x-3\right)\left(2x+1\right)\)