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1 tháng 2
a: \(x^3-9x^2+6x+16\)
\(=x^3-8x^2-x^2+8x-2x+16\)
\(=x^2\left(x-8\right)-x\left(x-8\right)-2\left(x-8\right)\)
\(=\left(x-8\right)\left(x^2-x-2\right)\)
\(=\left(x-8\right)\left(x-2\right)\left(x+1\right)\)
b: \(x^3-x^2-x-2\)
\(=x^3-2x^2+x^2-2x+x-2\)
\(=x^2\left(x-2\right)+x\left(x-2\right)+\left(x-2\right)\)
\(=\left(x-2\right)\cdot\left(x^2+x+1\right)\)
c: \(x^3+x^2-x+2\)
\(=x^3+2x^2-x^2-2x+x+2\)
\(=x^2\left(x+2\right)-x\left(x+2\right)+\left(x+2\right)\)
\(=\left(x+2\right)\left(x^2-x+1\right)\)
d: \(x^3-6x^2-x+30\)
\(=x^3+2x^2-8x^2-16x+15x+30\)
\(=x^2\left(x+2\right)-8x\left(x+2\right)+15\left(x+2\right)\)
\(=\left(x+2\right)\left(x^2-8x+15\right)\)
\(=\left(x+2\right)\left(x-3\right)\left(x-5\right)\)
e: Sửa đề: \(x^3-7x-6\)
\(=x^3-x-6x-6\)
\(=x\left(x^2-1\right)-6\left(x+1\right)\)
\(=x\left(x-1\right)\left(x+1\right)-6\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-x-6\right)\)
\(=\left(x+1\right)\left(x-3\right)\left(x+2\right)\)
f: \(27x^3-27x^2+18x-4\)
\(=27x^3-9x^2-18x^2+6x+12x-4\)
\(=9x^2\left(3x-1\right)-6x\left(3x-1\right)+4\left(3x-1\right)\)
\(=\left(3x-1\right)\left(9x^2-6x+4\right)\)
g: \(2x^3-x^2+5x+3\)
\(=2x^3+x^2-2x^2-x+6x+3\)
\(=x^2\left(2x+1\right)-x\left(2x+1\right)+3\left(2x+1\right)\)
\(=\left(2x+1\right)\left(x^2-x+3\right)\)
h: \(\left(x^2-3\right)^2+16\)
\(=x^4-6x^2+9+16\)
\(=x^4-6x^2+25\)
\(=x^4+10x^2+25-16x^2\)
\(=\left(x^2+5\right)^2-\left(4x\right)^2\)
\(=\left(x^2+5+4x\right)\left(x^2+5-4x\right)\)
T
17 tháng 10 2023
\(x^3-9x^2+6x+16\\=x^3+x^2-10x^2-10x+16x+16\\=x^2(x+1)-10x(x+1)+16(x+1)\\=(x+1)(x^2-10x+16)\\=(x+1)(x^2-2x-8x+16)\\=(x+1)[x(x-2)-8(x-2)]\\=(x+1)(x-2)(x-8)\\Toru\)
15 tháng 11 2021
\(=x^2-6x+9-2=\left(x-3\right)^2-2=\left(x-3-\sqrt{2}\right)\left(x-3+\sqrt{2}\right)\)
HN
1
18 tháng 8 2017
\(x^3+9x^2+6x-16\)
\(=x^3+x^2-2x+8x^2+8x-16\)
\(=x\left(x^2+x-2\right)+8\left(x^2+x-2\right)\)
\(=\left(x^2+x-2\right)\left(x+8\right)\)
\(=\left(x^2-x+2x-2\right)\left(x+8\right)\)
\(=\left[x\left(x-1\right)+2\left(x-1\right)\right]\left(x+8\right)\)
\(=\left(x-1\right)\left(x+2\right)\left(x+8\right)\)
T
14 tháng 9 2018
\(x^3-9x^2+6x+16=x^3-8x^2-x^2+8x-2x+16\)
\(=x^2.\left(x-8\right)-x.\left(x-8\right)-2.\left(x-8\right)\)
\(=\left(x-8\right).\left(x^2-x-2\right)=\left(x-8\right).\left(x^2-2x+x-2\right)\)
\(=\left(x+8\right)\left[x.\left(x-2\right)+\left(x-2\right)\right]\)
\(=\left(x+8\right).\left(x-2\right)\left(x+1\right)\)
14 tháng 9 2018
\(x^3-9x^2+6x+16\)
\(=\left(x^3+x^2\right)-\left(10x^2+10x\right)+\left(16x+16\right)\)
\(=x^2.\left(x+1\right)-10x\left(x+1\right)+16\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-10x+16\right)\)
Tham khảo nhé~
NV
2
23 tháng 11 2021
\(=x^2\left(x-6\right)-24\left(x-6\right)=\left(x^2-24\right)\left(x-6\right)\)
HN
1
NN
13 tháng 10 2020
\(x^3-9x^2+6x+16=\left(x^3+x^2\right)-\left(10x^2+10x\right)+\left(16x+16\right)\)
\(=x^2.\left(x+1\right)-10x\left(x+1\right)+16\left(x+1\right)\)
\(=\left(x+1\right).\left(x^2-10x+16\right)\)
\(=\left(x+1\right).\left[\left(x^2-8x\right)-\left(2x-16\right)\right]\)
\(=\left(x+1\right)\left[x\left(x-8\right)-2\left(x-8\right)\right]\)
\(=\left(x+1\right)\left(x-2\right)\left(x-8\right)\)
NT
13 tháng 10 2014
x^3-9x^2+6x+16
=x^3+x^2-10x^2-10x+16x+16
=(x^3+x^2)-(10x^2+10x)+(16x+16)
=x^2(x+1)-10x(x+1)+16(x+1)
=(x+1)(x^2-10x+16)
=(x+1)(x^2-2x-8x+16)
=(x+1)[(x^2-2x)-(8x-16)]
=(x+1)[x(x-2)-8(x-2)]
=(x+1)(x-2)(x-8)
x^3 -9x^2 +6x +16
<=>x3 - 8x2 - x2 + 8x - 2x + 16
<=>x2(x -8) - x(x - 8) - 2(x - 8)
<=>(x - 8)(x2 - x - 2)
<=> (x - 8)(x + 1)(x - 2)