phân tích đa thức thành nhân tử
a)x(x-5)+(5-x)2
b) x2-20x+100
c) x2+5x+6
giúp mik với mik đag cần gấp
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Khách
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25 tháng 8 2021
a) \(x^2\left(x^2+4\right)-x^2-4=x^2\left(x^2+4\right)-\left(x^2+4\right)=\left(x^2+4\right)\left(x^2-1\right)=\left(x^2+4\right)\left(x-1\right)\left(x+1\right)\)
b) \(\left(x^2+x\right)^2+4x^2+4x-12=\left(x^2+x\right)^2+4\left(x^2+x\right)+4-16=\left(x^2+x+2\right)^2-4^2=\left(x^2+x+2-4\right)\left(x^2+x+2+4\right)=\left(x^2+x-2\right)\left(x^2+x+6\right)=\left(x-1\right)\left(x+2\right)\left(x^2+x+6\right)\)
c) \(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24=\left(x^2+7x+10\right)^2+2\left(x^2+7x+10\right)+1-25=\left(x^2+7x+11\right)^2-5^2=\left(x^2+7x+11-5\right)\left(x^2+7x+11+5\right)=\left(x^2+7x+6\right)\left(x^2+7x+16\right)=\left(x+1\right)\left(x+6\right)\left(x^2+7x+16\right)\)
NT
25 tháng 8 2021
a. \(x^2\left(x^2+4\right)-x^2-4\)
\(=x^2\left(x^2+4\right)-\left(x^2+4\right)\)
\(=\left(x^2-1\right)\left(x^2+4\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(x^2+4\right)\)
b. \(\left(x^2+x\right)^2+4x^2+4x-12\)
\(=x^4+2x^3+5x^2+4x-12\)
\(=\left(x-1\right)\left(x+2\right)\left(x^2+x+6\right)\)
c. \(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24\)
\(=\left(x+2\right)\left(x+5\right)\left(x+3\right)\left(x+4\right)-24\)
\(=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24\) (*)
Đặt \(t=x^2+7x+10\), ta được
(*) \(=t\left(t+2\right)-24\)
\(=t^2+2t-24\)
\(=\left(t-4\right)\left(t+6\right)\)
hay \(\left(x^2+7x+6\right)\left(x^2+7x+18\right)\)
NH
1
31 tháng 7 2021
a) \(9-\left(x-y\right)^2=\left(3-x+y\right)\left(3+x-y\right)\)
b) \(x^2+6x+9-y^2=\left(x+3\right)^2-y^2=\left(x+y+3\right)\left(x-y+3\right)\)
TL
3
18 tháng 11 2021
\(a,=3xyz\left(x+2\right)\\ b,=5\left(x+2\right)-x\left(x+2\right)=\left(x+2\right)\left(5-x\right)\\ c,=\left(x+y\right)^2-z^2=\left(x+y-z\right)\left(x+y+z\right)\)
18 tháng 11 2021
a) 3x2yz + 6xyz = 3xyz(x+2)
b) 5(x+2) - x2 - 2x = 5(x+2) - x(x+2) = (5+x)(x+2)
c) x2 + 2xy + y2 - 22 = (x2+2xy+y2) - 22 = (x+y)2 - 22 = (x+y+2)(x+y-2)
27 tháng 9 2021
a) \(=x^4-14x^2+40-72=x^4-14x^2-32=\left(x-4\right)\left(x+4\right)\left(x^2+2\right)\)
b) \(=\left(x^2+5x+4\right)\left(x^2+5x+6\right)+1=\left(x^2+5x\right)^2+2\left(x^2+5x\right)+1=\left(x^2+5x+1\right)^2\)
c) \(=x^4+3x^3-3x^2+3x^3+9x^2-9x+x^2+3x-3-5=x^4+6x^3+7x^2-6x-8=\left(x-1\right)\left(x+1\right)\left(x+2\right)\left(x+4\right)\)
27 tháng 9 2021
a: Ta có: \(\left(x^2-4\right)\left(x^2-10\right)-72\)
\(=x^4-14x^2-32\)
\(=\left(x^2-16\right)\left(x^2+2\right)\)
\(=\left(x-4\right)\left(x+4\right)\left(x^2+2\right)\)
b: Ta có: \(\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)+1\)
\(=\left(x^2+5x+6\right)\left(x^2+5x+4\right)+1\)
\(=\left(x^2+5x\right)^2+10\left(x^2+5x\right)+24+1\)
\(=\left(x^2+5x+1\right)^2\)
T
1
LL
1
15 tháng 9 2021
\(a,=\left(x-1\right)^4-2\left(x-1\right)^2+1\\ =\left[\left(x-1\right)^2-1\right]^2\\ =\left(x^2-2x-2\right)^2\\ b,=\left[\left(x+1\right)\left(x+5\right)\right]\left[\left(x+2\right)\left(x+4\right)\right]-4\\ =\left(x^2+6x+5\right)\left(x^2+6x+8\right)-4\\ =\left(x^2+6x\right)^2+13\left(x^2+6x\right)+36\\ =\left(x^2+6x+4\right)\left(x^2+6x+9\right)\\ =\left(x+3\right)^2\left(x^2+6x+4\right)\)
21 tháng 10 2021
\(a,=x-x^2=x\left(1-x\right)\\ b,=x^2+3x-2x-6=\left(x+3\right)\left(x-2\right)\\ c,=x^2+2x+3x+6=\left(x+2\right)\left(x+3\right)\)
21 tháng 10 2021
a) \(x^2-2x^2+x=-x^2+x=-x\left(x-1\right)\)
b) \(x^2+x-6=\left(x^2+3x\right)-\left(2x+6\right)=x\left(x+3\right)-2\left(x+3\right)=\left(x-2\right)\left(x+3\right)\)
c) \(x^2+5x+6=\left(x^2+2x\right)+\left(3x+6\right)=x\left(x+2\right)+3\left(x+2\right)=\left(x+2\right)\left(x+3\right)\)
a) \(=x\left(x-5\right)+\left(x-5\right)^2=\left(x-5\right)\left(x+x-5\right)=\left(x-5\right)\left(2x-5\right)\)
b) \(=x^2-2.x.10+10^2=\left(x-10\right)^2\)
c) \(=x\left(x+3\right)+2\left(x+3\right)=\left(x+3\right)\left(x+2\right)\)