Phân tích thành nhân tử:
x4 + (x - 4)4 - 82
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Khách
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NH
3
9 tháng 2 2021
Ta có : \(x^4-5x^2+4\)
\(=x^4-x^2-4x^2+4\)
\(=x^2\left(x^2-1\right)-4\left(x^2-1\right)\)
\(=\left(x^2-1\right)\left(x^2-4\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(x-2\right)\left(x+2\right)\)
9 tháng 2 2021
Ta có: \(x^4-5x^2+4\)
\(=x^4-x^2-4x^2+4\)
\(=x^2\left(x^2-1\right)-4\left(x^2-1\right)\)
\(=\left(x^2-1\right)\left(x^2-4\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(x-2\right)\left(x+2\right)\)
NT
2
29 tháng 8 2021
\(x^4+8x=x\left(x^3+8\right)=x\left(x+2\right)\left(x^2-2x+4\right)\)
HD
3
D
10 tháng 8 2021
x4−2x3+2x−1x4−2x3+2x−1
=x4−x3−x3+x2−x2+x+x−1=x4−x3−x3+x2−x2+x+x−1
=x3(x−1)−x2(x−1)−x(x−1)+(x−1)=x3(x−1)−x2(x−1)−x(x−1)+(x−1)
=(x−1)(x3−x2−x+1)=(x−1)(x3−x2−x+1)
=(x−1)[
10 tháng 8 2021
\(x^4+2x^3+2x^2+2x+1\\ =\left(x^4+x^3\right)+\left(x^3+x^2\right)+\left(x^2+x\right)+\left(x+1\right)\\ =x^3\left(x+1\right)+x^2\left(x+1\right)+x\left(x+1\right)+\left(x+1\right)\\ =\left(x^3+x^2+x+1\right)\left(x+1\right)\\ =\left[\left(x^3+x^2\right)+\left(x+1\right)\right]\left(x+1\right)\\ =\left[x^2\left(x+1\right)+\left(x+1\right)\right]\left(x+1\right)\\ =\left(x^2+1\right)\left(x+1\right)^2\)
TL
0
V
5 tháng 7 2019
a)x4+(x-4)4-82
=x4-81+(x-4)4-1
=((x2)2-92) + (x-4)2+1)(x-4)2-1)
=(x2-9)(x2+9)+(x-4)2+1)(x-4-1)(x-4+1)
=(x-3)(x+3)(x2+9)+(x-4)2+1)(x-5)(x-3)
=(x-3)[(x3+9x+3x2+27)+(x2-8x+14+1)(x-5)]
=(x-3)[(x3+9x+3x2+27)+(x3-5x2-8x2+40x+14x-70+x-5)]
=(x-3)(2x3-10x2+64x-48)
b)(x2-a)2-6x2+4x+2a
=[(x2-a)2-4x2]-[2x2+4x-2a]
=(x2-a-2x)-2(x2+2x+a)
=-(x2+a+2x)-2(x2+2x+a)
=-3(x2+2x+a)
DT
1
6 tháng 11 2021
\(1,=x\left(x^2-2x+1-y^2\right)=x\left[\left(x-1\right)^2-y^2\right]=x\left(x-y-1\right)\left(x+y-1\right)\\ 2,=\left(x+y\right)^3\\ 3,=\left(2y-z\right)\left(4x+7y\right)\\ 4,=\left(x+2\right)^2\\ 5,Sửa:x\left(x-2\right)-x+2=0\\ \Leftrightarrow\left(x-2\right)\left(x-1\right)=0\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)
M
1
19 tháng 11 2023
1: Đa thức này ko phân tích được nha bạn
2: \(x^2+8x+7\)
\(=x^2+x+7x+7\)
\(=x\left(x+1\right)+7\left(x+1\right)\)
\(=\left(x+1\right)\left(x+7\right)\)
3: \(x^2-6x-16\)
\(=x^2-8x+2x-16\)
\(=x\left(x-8\right)+2\left(x-8\right)\)
\(=\left(x-8\right)\left(x+2\right)\)
4: \(4x^2-8x+3\)
\(=4x^2-2x-6x+3\)
\(=2x\left(2x-1\right)-3\left(2x-1\right)\)
\(=\left(2x-1\right)\left(2x-3\right)\)
5: \(3x^2-11x+6\)
\(=3x^2-9x-2x+6\)
\(=3x\left(x-3\right)-2\left(x-3\right)\)
\(=\left(x-3\right)\left(3x-2\right)\)
\(x^4+\left(x-4\right)^4-82\)
\(=\left(x^4-1\right)+\left[\left(x-4\right)^4-81\right]\)
\(=\left(x^2+1\right)\left(x^2-1\right)+\left[\left(x^2-4x+4-9\right)\left(x^2-4x+4+9\right)\right]\)
\(=\left(x^2+1\right)\left(x+1\right)\left(x-1\right)+\left(x^2-4x-5\right)\left(x^2-4x+13\right)\)
\(=\left(x^2+1\right)\left(x+1\right)\left(x-1\right)+\left(x^2+x-5x-5\right)\left(x^2-4x+13\right)\)
\(=\left(x^2+1\right)\left(x+1\right)\left(x-1\right)+\left(x+1\right)\left(x-5\right)\left(x^2-4x+13\right)\)
\(=\left(x+1\right)\left[\left(x^2+1\right)\left(x-1\right)+\left(x-5\right)\left(x^2-4x+13\right)\right]\)
\(=\left(x+1\right)\left(x^3-x^2+x-1+x^3-4x^2+13x-5x^2+20x-65\right)\)
\(=\left(x+1\right)\left(2x^3-10x^2+34x-66\right)\)
\(=\left(x+1\right)\left(2x^3-6x^2-4x^2+12x+22x-66\right)\)
\(=\left(x+1\right)\left[2x^2\left(x-3\right)-4x\left(x-3\right)+22\left(x-3\right)\right]\)
\(=\left(x+1\right)\left(x-3\right)\left(2x^2-4x+22\right)\)