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LT
1
21 tháng 7 2016
Ta có : \(M=\left(x^2+3x+2\right)\left(x^2+7x+12\right)+1=\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)+1\)
\(=\left[\left(x+1\right)\left(x+4\right)\right].\left[\left(x+2\right)\left(x+3\right)\right]+1=\left(x^2+5x+4\right)\left(x^2+5x+6\right)+1\)
Đặt \(t=x^2+5x+5\) \(\Rightarrow M=\left(t-1\right)\left(t+1\right)+1=t^2-1+1=t^2\)
Vậy \(M=\left(x^2+5x+5\right)^2\)
14 tháng 8 2018
\(3x^2+7x+2\)
\(=3x^2+6x+x+2\)
\(=3x\left(x+2\right)+\left(x+2\right)\)
\(=\left(3x+1\right)\left(x+2\right)\)
14 tháng 8 2018
\(3x^2+7x+2\)
\(=3x^2+x+6x+2\)
\(=x\left(3x+1\right)+2\left(3x+1\right)\)
\(=\left(3x+1\right).\left(x+2\right)\)
MT
1
12 tháng 7 2017
\(3x^3-7x^2+17x-5.\)
\(=3x^3-x^2-6x^2+2x-15x+5\)
\(=\left(3x^3-x^2\right)-\left(6x^2-2x\right)-\left(15x-5\right)\)
\(=x^2\left(3x-1\right)-2x\left(3x-1\right)-5\left(3x-1\right)\)
\(=\left(3x-1\right)\left(x^2-2x-5\right)\)
C2
1
14 tháng 8 2015
7x2 - 28 = 7(x2 - 4) = 7(x - 2)(x + 2)
2x3 + 3x2 - 18x - 27 = x2(2x + 3) - 9(2x + 3) = (2x + 3)(x2 - 9) = (2x + 3)(x - 3)(x + 3)
NQ
1
8 tháng 10 2015
B= 2x^2+2x+3x+3
= 2x(x+1)+3(x+1)
=(x+1)( 2x+3)
C=3x^2-6x-x+2
=3x(x-2)-(x-2)
=(x-2)(3x-1)
NT
1
19 tháng 7 2017
\(=\left(x+1\right)\left(x-2\right)\left(2x^2-x-4\right)\)
NT
3
23 tháng 11 2017
\(=\left(2x^4+6x^3\right)-\left(3x^3+9x^2\right)-\left(3x^2-9x\right)+\left(2x+6\right)\)
\(=\left(x+3\right)\left(2x^3-3x^2-3x+2\right)=\left(x+3\right)\left(2x^3-4x^2+x^2-2x-x+2\right)\)
\(=\left(x+3\right)\left(x-2\right)\left(2x^2+x-1\right)=\left(x+3\right)\left(x-2\right)\left(2x^2+2x-x-1\right)\)
\(\left(x+3\right)\left(x-2\right)\left(x+1\right)\left(2x-1\right)\)
PT
1
16 tháng 10 2018
\(x^4+3x^2+36\)
\(=\left(x^2\right)^2+2.x^2.6+6^2-9x^2\)
\(=\left(x^2+6\right)^2-\left(3x\right)^2=\left(x^2-3x+6\right)\left(x^2+3x+6\right)\)
\(2x^4-3x^3-7x^2+6x+8\)
\(=2x^4+2x^3-5x^3-5x^2-2x^2-2x+8x+8\)
\(=2x^3\left(x+1\right)-5x^2\left(x+1\right)-2x\left(x+1\right)+8\left(x+1\right)\)
\(=\left(x+1\right)\left(2x^3-5x^2-2x+8\right)\)
\(=\left(x+1\right)\left[2x^2\left(x-2\right)-x\left(x-2\right)-4\left(x-2\right)\right]\)
\(=\left(x+1\right)\left(x-2\right)\left(2x^2-x-4\right)\)
Chúc bạn học tốt.
6 tháng 9 2020
a) \(x^2-5x+6=x^2-2x-3x+6=\left(x-2\right)\left(x-3\right)\)
b)\(3x^2+9x-30=3x^2-6x+15x-30=3\left(x-2\right)\left(x+5\right)\)
c)\(x^2-7x+12=x^2-3x-4x+12=\left(x-3\right)\left(x-4\right)\)
d)\(x^2-7x+10=x^2-2x-5x+10=\left(x-2\right)\left(x-5\right)\)
NN
6 tháng 9 2020
a) \(x^2-5x+6=x^2-2x-3x+6=\left(x^2-2x\right)-\left(3x-6\right)\)
\(=x\left(x-2\right)-3\left(x-2\right)=\left(x-2\right)\left(x-3\right)\)
b) \(3x^2+9x-30=3\left(x^2+3x-10\right)=3\left(x^2-2x+5x-10\right)\)
\(=3\left[\left(x^2-2x\right)+\left(5x-10\right)\right]=3\left[x\left(x-2\right)+5\left(x-2\right)\right]\)
\(=3\left(x-2\right)\left(x+5\right)\)
c) \(x^2-7x+12=x^2-3x-4x+12=\left(x^2-3x\right)-\left(4x-12\right)\)
\(=x\left(x-3\right)-4\left(x-3\right)=\left(x-3\right)\left(x-4\right)\)
d) \(x^2-7x+10=x^2-2x-5x+10=\left(x^2-2x\right)-\left(5x-10\right)\)
\(=x\left(x-2\right)-5\left(x-2\right)=\left(x-2\right)\left(x-5\right)\)
Dễ mà ^_^: 3x2-7x+2=3x2 -x-6x+2=(3x2-x)-(6x-2)=x(3x-1)-2(3x-1)=(3x-1)(x-2)
\(3x^2-7x+2=\left(3x^2-6x\right)-\left(x-2\right)=3x\left(x-2\right)-\left(x-2\right)=\left(3x-1\right)\left(x-2\right)\)