Phân tích thành nhân tử :
a, \(x^4+3x^3-7x^2-27x-18\)
b, \(x^4+5x^3-7x^2-41x-30\)
c, \(x^6-14x^4+49x^2-36\)
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PO
1
25 tháng 5 2022
c: \(x^3-8x^2+x+42\)
\(=x^3+2x^2-10x^2-20x+21x+42\)
\(=\left(x+2\right)\left(x^2-10x+21\right)\)
\(=\left(x+2\right)\left(x-3\right)\left(x-7\right)\)
a: \(x^3+6x^2+11x+6\)
\(=x^3+3x^2+3x^2+9x+2x+6\)
\(=\left(x+3\right)\left(x^2+3x+2\right)\)
\(=\left(x+3\right)\left(x+1\right)\left(x+2\right)\)
8 tháng 10 2016
b) 3x4-3x3+9x3-9x2-24x2+24x-48x+48
=3x3(x-1)+9x2(x-1)-24x(x-1)-48(x-1)
=(x-1)(3x3+9x2-24x-48)
=3(x-1)(x3+3x2-8x-16)
29 tháng 8 2023
a: x^3-7x-6
=x^3-x-6x-6
=x(x-1)(x+1)-6(x+1)
=(x+1)(x^2-x-6)
=(x-3)(x+2)(x+1)
b: =2x^3+x^2-2x^2-x+6x+3
=x^2(2x+1)-x(2x+1)+3(2x+1)
=(2x+1)(x^2-x+3)
c: =2x^3-3x^2-2x^2+3x+2x-3
=x^2(2x-3)-x(2x-3)+(2x-3)
=(2x-3)(x^2-x+1)
d: =2x^3+x^2+2x^2+x+2x+1
=(2x+1)(x^2+x+1)
e: =3x^3+x^2-3x^2-x+6x+2
=(3x+1)(x^2-x+2)
f: =27x^3-9x^2-18x^2+6x+12x-4
=(3x-1)(9x^2-6x+4)
H9
HT.Phong (9A5)
CTVHS
29 tháng 8 2023
a) \(x^3-7x-6\)
\(=x^3-x-6x-6\)
\(=\left(x^3-x\right)-\left(6x+6\right)\)
\(=x\left(x^2-1\right)-6\left(x+1\right)\)
\(=x\left(x+1\right)\left(x-1\right)-6\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-x-6\right)\)
b) \(2x^3-x^2+5x+3\)
\(=2x^3+x^2-2x^2-x+6x+3\)
\(=\left(2x^3+x^2\right)-\left(2x^2+x\right)+\left(6x+3\right)\)
\(=x^2\left(2x+1\right)-x\left(2x+1\right)+3\left(2x+1\right)\)
\(=\left(x^2-x+3\right)\left(2x+1\right)\)
c) \(2x^3-5x^2+5x+1\)
\(=2x^3-3x^2-2x^2+3x+2x-3\)
\(=\left(2x^3-3x^2\right)-\left(2x^2-3x\right)+\left(2x-3\right)\)
\(=x^2\left(2x-3\right)-x\left(2x-3\right)+\left(2x-3\right)\)
\(=\left(x^2-x+1\right)\left(2x-3\right)\)
d) \(2x^3+3x^2+3x+1\)
\(=2x^3+x^2+2x^2+x+2x+1\)
\(=\left(2x^3+x^2\right)+\left(2x^2+x\right)+\left(2x+1\right)\)
\(=x^2\left(2x+1\right)+x\left(2x+1\right)+\left(2x+1\right)\)
\(=\left(2x+1\right)\left(x^2+x+1\right)\)
e) \(3x^3-2x^2+5x+2\)
\(=3x^3+x^2-3x^2-x+6x+2\)
\(=\left(3x^3+x^2\right)-\left(3x^2+x\right)+\left(6x+2\right)\)
\(=x^2\left(3x+1\right)-x\left(3x+1\right)+2\left(3x+1\right)\)
\(=\left(3x-1\right)\left(x^2-x+2\right)\)
f) \(27x^3-27x^2+18x-4\)
\(=27x^3-9x^2-18x^2+6x+12x-4\)
\(=\left(27x^3-9x^2\right)-\left(18x^2-6x\right)+\left(12x-4\right)\)
\(=9x^2\left(3x-1\right)-6x\left(3x-1\right)+4\left(3x-1\right)\)
\(=\left(3x-1\right)\left(9x^2-6x+4\right)\)
PN
0
NL
1
BN
2
28 tháng 10 2020
a) Ta có: \(x^4+3x^3-7x^2-27x-18\)
\(=x^4-3x^3+6x^3-18x^2+11x^2-33x+6x-18\)
\(=x^3\left(x-3\right)+6x^2\left(x-3\right)+11x\left(x-3\right)+6\left(x-3\right)\)
\(=\left(x-3\right)\left(x^3+6x^2+11x+6\right)\)
\(=\left(x-3\right)\left(x^3+x^2+5x^2+5x+6x+6\right)\)
\(=\left(x-3\right)\left[x^2\left(x+1\right)+5x\left(x+1\right)+6\left(x+1\right)\right]\)
\(=\left(x-3\right)\left(x+1\right)\left(x^2+5x+6\right)\)
\(=\left(x-3\right)\left(x+1\right)\left(x+2\right)\left(x+3\right)\)
b) Ta có: \(x^3-8x^2+x+42\)
\(=x^3-7x^2-x^2+7x-6x+42\)
\(=x^2\left(x-7\right)-x\left(x-7\right)-6\left(x-7\right)\)
\(=\left(x-7\right)\left(x^2-x-6\right)\)
\(=\left(x-7\right)\left(x-3\right)\left(x+2\right)\)
c) Ta có: \(x^4+5x^3-7x^2-41x-30\)
\(=x^4+5x^3-7x^2-35x-6x-30\)
\(=x^3\left(x+5\right)-7x\left(x+5\right)-6\left(x+5\right)\)
\(=\left(x+5\right)\left(x^3-7x-6\right)\)
\(=\left(x+5\right)\left(x^3-x-6x-6\right)\)
\(=\left(x+5\right)\left[x\left(x^2-1\right)-6\left(x+1\right)\right]\)
\(=\left(x+5\right)\left[x\left(x-1\right)\left(x+1\right)-6\left(x+1\right)\right]\)
\(=\left(x+5\right)\left(x+1\right)\left(x^2-x-6\right)\)
\(=\left(x+5\right)\left(x+1\right)\left(x-3\right)\left(x+2\right)\)
K
28 tháng 10 2020
a ) \(==>x^3.\left(x+3\right)-\left(7x^2+27x+18\right)\)
ko xét phần x^3.( x+3 ) nữa mà mik phân tích trong ngoặc nha zo thi ko lm như vậy mà ghi lại phần đó nha
\(7x^2+21x+6x+18\)
\(7x\left(x+3\right)+6\left(x+3\right)\)
\(\left(x+3\right)\left(7x+6\right)\)
==> \(x^3.\left(x+3\right)-\left(x+3\right)\left(7x+6\right)\)
==>\(\left(x+3\right)\left(x^3-7x-6\right)\)
PA
16 tháng 10 2016
\(2x^2+3x-27=2x^2-6x+9x-27=2x\left(x-3\right)+9\left(x-3\right)=\left(2x+9\right)\left(x-3\right)\)
\(x^3-7x+6=x^3-x-6x+6=x\left(x^2-1\right)-6\left(x-1\right)=x\left(x-1\right)\left(x+1\right)-6\left(x-1\right)=\left(x-1\right)\left(x^2+x-6\right)\)
\(x^3+5x^2+8x+4=x^3+x^2+4x^2+8x+4=x^2\left(x+1\right)+4\left(x^2+2x+1\right)=x^2\left(x+1\right)+4\left(x+1\right)^2\)
\(=\left(x+1\right)\left(x^2+4x+4\right)=\left(x+1\right)\left(x+2\right)^2\)
\(27x^3-27x^2+18x-4=27x^3-9x^2-18x^2+6x+12x-4\)
\(=9x^2\left(3x-1\right)-6x\left(3x-1\right)+4\left(3x-1\right)=\left(3x-1\right)\left(9x^2-6x+4\right)\)
NN
2
3 tháng 8 2017
a)\(\left(x+1\right)\left(x+2\right)\left(x+3\right)\)
b)\(\left(x-3\right)\left(x-7\right)\left(x+2\right)\)
c)\(\left(x-3\right)\left(x+3\right)\left(x+2\right)\left(x+1\right)\)
d)\(\left(x+5\right)\left(x-3\right)\left(x+1\right)\left(x+2\right)\)
a) \(x^4+3x^3-7x^2-27x-18\)
\(=\left(x^4+3x^3+2x^2\right)-\left(9x^2-27x-18\right)\)
\(=x^2\left(x^2+3x+2\right)-9\left(x^2+3x+2\right)=\left(x^2+x+2x+2\right)\left(x^2-9\right)\)
\(=\left(x+1\right)\left(x+2\right)\left(x-3\right)\left(x+3\right)\)
b) \(x^4+5x^3-7x^2-41x-30\)
\(=\left(x^4+2x^3-15x^2\right)+\left(3x^3+6x^2-45x\right)+\left(2x^2+4x-30\right)\)
\(=x^2\left(x^2+2x-15\right)+3x\left(x^2+2x-15\right)+2\left(x^2+2x-15\right)\)
\(=\left(x^2+2x-15\right)\left(x^2+3x+2\right)=\left(x^2+5x-3x-15\right)\left(x^2+x+2x+2\right)\)
\(=\left(x+5\right)\left(x-3\right)\left(x+1\right)\left(x+2\right)\)
c) \(x^6-14x^4+49x^2-36\)
\(=\left(x^6-9x^4\right)+\left(-5x^4+45x^2\right)+\left(4x^2-36\right)\)
\(=x^4\left(x^2-9\right)-5x^2\left(x^2-9\right)+4\left(x^2-9\right)\)
\(=\left(x^2-9\right)\left(x^4-5x^2+4\right)=\left(x^2-9\right)\left(x^4-4x^2-x^2+4\right)\)
\(=\left(x^2-1\right)\left(x^2-4\right)\left(x^2-9\right)=\left(x-1\right)\left(x+1\right)\left(x-2\right)\left(x+2\right)\left(x-3\right)\left(x+3\right)\)