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KL
3
BT
1
2 tháng 8 2018
(x2 + x + 2)(x2 + 9x + 18) - 28
= x4 + 10x3 + 29x2 + 36x + 36 - 28
= x4 + 10x3 + 29x2 + 36x + 8
TN
1
NV
Nguyễn Việt Lâm
Giáo viên
12 tháng 12 2021
\(x^3-9x^2+x=x\left(x^2-9x+1\right)\)
\(x^3+13x^2+x=x\left(x^2+13x+1\right)\)
4 tháng 9 2018
d, \(x^8+x^7+1\)
\(=x^8-x^2+x^7-x+x^2+x+1\)
\(=x^2\left(x^6-1\right)+x\left(x^6-1\right)+x^2+x+1\)
\(=x^2\left(x^3-1\right)\left(x^3+1\right)+x\left(x^3-1\right)\left(x^3+1\right)+x^2+x+1\)
\(=\left(x^5+x^2\right)\left(x^3-1\right)+\left(x^4+x\right)\left(x^3-1\right)+x^2+x+1\)
\(=\left(x^3-1\right)\left(x^5+x^4+x^2+x\right)+x^2+x+1\)
\(=\left(x^2+x+1\right)\left(x-1\right)\left(x^5+x^4+x^2+x\right)+x^2+x+1\)
\(=\left(x^2+x+1\right)\left(x^6-x^4+x^3-x\right)+x^2+x+1\)
\(=\left(x^2+x+1\right)\left(x^6-x^4+x^3-x+1\right)\)
c, \(x^4+5x^3-12x^2+5x+1\)
\(=x^4-x^3+6x^3-6x^2-6x^2+6x-x+1\)
\(=x^3\left(x-1\right)+6x^2\left(x-1\right)-6x\left(x-1\right)-\left(x-1\right)\)
\(=\left(x-1\right)\left[x^3+6x^2-6x-1\right]\)
\(=\left(x-1\right)\left[\left(x-1\right)\left(x^2+x+1\right)+6x\left(x-1\right)\right]\)
\(=\left(x-1\right)\left(x-1\right)\left(x^2+7x+1\right)\)
\(=\left(x-1\right)^2.\left(x^2+7x+1\right)\)
a, \(\left(x^2+x-2\right)\left(x^2+9x+18\right)-28\)
\(=\left(x-1\right)\left(x+2\right)\left(x+3\right)\left(x+6\right)-28\)
\(=\left[\left(x-1\right)\left(x+6\right)\right].\left[\left(x+2\right)\left(x+3\right)\right]-28\)
\(=\left(x^2+5x-6\right)\left(x^2+5x+6\right)-28\)
\(=\left(x^2+5x\right)^2-36-28\)
\(=\left(x^2+5x\right)^2-64\)
\(=\left(x^2+5x-8\right)\left(x^2+5x+8\right)\)
b, \(B=\left(x+1\right)^2\left(2x+3\right)-18\)
\(=\left(4x^2+8x+3\right)\left(x^2+2x+1\right)-18\)
Đặt \(x^2+2x+1=t\Rightarrow4x^2+8x+3=4t-1\)
Ta có: \(B=\left(4t-1\right)t-18\)
\(=4t^2-t-18\)
\(=4t^2-9t+8t-18\)
\(=t\left(4t-9\right)+2\left(4t-9\right)\)
\(=\left(4t-9\right)\left(t+2\right)\)
\(=\left(4x^2+8x-5\right)\left(x^2+2x+3\right)\) (vì \(t=x^2+2x+1\)
\(=\left(2x-1\right)\left(2x+5\right)\left(x^2+2x+3\right)\)
Chúc bạn học tốt.
19 tháng 10 2018
a) \(x^2-9x+14\)
\(=x^2-2x-7x+14\)
\(=x\left(x-2\right)-7\left(x-2\right)\)
\(=\left(x-2\right)\left(x-7\right)\)
b) \(x^2+17x-18\)
\(=x^2+18x-x-18\)
\(=x\left(x+18\right)-\left(x+18\right)\)
\(=\left(x+18\right)\left(x-1\right)\)
c) \(2x^2-7x+3\)
\(=2x^2-x-6x+3\)
\(=x\left(2x-1\right)-3\left(2x-1\right)\)
\(=\left(2x-1\right)\left(x-3\right)\)
d) \(x^2-25x+144\)
\(=x^2-9x-16x+144\)
\(=x\left(x-9\right)-15\left(x-9\right)\)
\(=\left(x-9\right)\left(x-15\right)\)
BC
1
4 tháng 3 2021
\(\Rightarrow\left(x^2+2x\right)^2+9\left(x^2+2x\right)+20=\left(x^2+2x\right)^2+4\left(x^2+2x\right)+5\cdot\left(x^2+2x\right)+20=\left(x^2+2x\right)\left(x^2+2x+4\right)+5\left(x^2+2x+4\right)=\left(x^2+2x+4\right)\left(x^2+2x+5\right)\)