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S
23 tháng 12 2016
a, \(x^4+6x^3+7x^2-6x+1\)
\(=x^4-2x^2+1+6x^3+9x^2+6x\)
\(=\left(x^2-1\right)^2+6x\left(x^2-1\right)+9x^2\)
\(=\left(x^2-1+3x\right)^2\)
b, \(x^4-7x^3+14x^2-7x+1\)
\(=x^4+2x^2+1+7x^3+12x^2-7x\)
\(=\left(x^2+1\right)^2-7x\left(x^2+1\right)+12^2\)
\(=\left(x^2-1+3x\right)^2\)
c, \(12x^2-11x-36\)
\(=12x^2-27x+16x-36\)
\(=3x\left(4x-9\right)+4\left(4x-9\right)\)
\(=\left(4x-9\right)\left(3x+4\right)\)
SM
15 tháng 9 2018
x4 - 7x3 + 14x2 - 7x + 1
= x4 - 3x3 + x2 - 4x3 + 12x2 - 4x + x2 - 3x + 1
= x2 ( x2 - 3x + 1 ) - 4x ( x2 - 3x + 1 ) + ( x2 - 3x + 1 )
= ( x2 - 3x + 1 ) ( x2 - 4x + 1 )
Q
6 tháng 6 2017
c) \(\left(x+1\right)^4+\left(x^2+x+1\right)^2\)
\(=\left(x+1\right)^4+x^4+x^2+1+2x^3+2x^2+2x\)
\(=\left(x+1\right)^4+x^4+3x^2+1+2x^3+2x\)
7 tháng 3 2019
a) \(x^4-7x^3+14x^2-7x+1\)(1)
Giả sử x khác 0, khi đó :
\(\left(1\right)\Leftrightarrow x^2\left(x^2-7x+14-\dfrac{7}{x}+\dfrac{1}{x^2}\right)\)
\(\Leftrightarrow x^2\left[\left(x^2+\dfrac{1}{x^2}\right)-7\left(x+\dfrac{1}{x}\right)+14\right]\)
\(\Leftrightarrow x^2\left[\left(x^2+2\cdot x\cdot\dfrac{1}{x}+\dfrac{2}{x^2}\right)-2-7\left(x+\dfrac{1}{x}\right)+14\right]\)
\(\Leftrightarrow x^2\left[\left(x+\dfrac{1}{x}\right)^2-7\left(x+\dfrac{1}{x}\right)+12\right]\)
Đặt \(x+\dfrac{1}{x}=a\)
pt \(\Leftrightarrow x^2\left(a^2-7a+12\right)\)
\(\Leftrightarrow x^2\left(a^2-3a-4a+12\right)\)
\(\Leftrightarrow x^2\left[a\left(a-3\right)-4\left(a-3\right)\right]\)
\(\Leftrightarrow x^2\left(a-3\right)\left(a-4\right)\)
\(\Leftrightarrow x^2\left(x+\dfrac{1}{x}-3\right)\left(x+\dfrac{1}{x}-4\right)\)
12 tháng 7 2016
a) \(x^4+3x^3-7x^2-27x-18\)
\(=\left(x^4+3x^3+2x^2\right)-\left(9x^2-27x-18\right)\)
\(=x^2\left(x^2+3x+2\right)-9\left(x^2+3x+2\right)=\left(x^2+x+2x+2\right)\left(x^2-9\right)\)
\(=\left(x+1\right)\left(x+2\right)\left(x-3\right)\left(x+3\right)\)
b) \(x^4+5x^3-7x^2-41x-30\)
\(=\left(x^4+2x^3-15x^2\right)+\left(3x^3+6x^2-45x\right)+\left(2x^2+4x-30\right)\)
\(=x^2\left(x^2+2x-15\right)+3x\left(x^2+2x-15\right)+2\left(x^2+2x-15\right)\)
\(=\left(x^2+2x-15\right)\left(x^2+3x+2\right)=\left(x^2+5x-3x-15\right)\left(x^2+x+2x+2\right)\)
\(=\left(x+5\right)\left(x-3\right)\left(x+1\right)\left(x+2\right)\)
c) \(x^6-14x^4+49x^2-36\)
\(=\left(x^6-9x^4\right)+\left(-5x^4+45x^2\right)+\left(4x^2-36\right)\)
\(=x^4\left(x^2-9\right)-5x^2\left(x^2-9\right)+4\left(x^2-9\right)\)
\(=\left(x^2-9\right)\left(x^4-5x^2+4\right)=\left(x^2-9\right)\left(x^4-4x^2-x^2+4\right)\)
\(=\left(x^2-1\right)\left(x^2-4\right)\left(x^2-9\right)=\left(x-1\right)\left(x+1\right)\left(x-2\right)\left(x+2\right)\left(x-3\right)\left(x+3\right)\)
4 tháng 11 2017
\(1.x^4+6x^3+11x^2+6x+1\)
\(=x^4+6x^3+9x^2+2x^2+6x+1\)
\(=x^4+9x^2+1+6x^3+2x^2+6x\)
\(=\left(x^2\right)^2+\left(3x\right)^2+1^2+2.x^2.3x+2.x^2.1+2.3x.1\)
\(=\left(x^2+3x+1\right)^2\)
\(2,6x^4+5x^3-38x^2+5x+6\)
\(=6x^4+6x^3+2x^3-3x^3-36x^2+2x^2-3x^2-x^2-12x+18x-x+6\)
\(=\left(6x^4+2x^3\right)+\left(6x^3+2x^2\right)-\left(3x^3+x^2\right)-\left(36x^2+12x\right)+\left(18x+6\right)-\left(3x^2+x\right)\)
\(=2x^3\left(3x+1\right)+2x^2\left(3x+1\right)-x^2\left(3x+1\right)-12x\left(3x+1\right)+6\left(3x+1\right)-x\left(3x+1\right)\)
\(=\left(3x+1\right)\left(2x^3+2x^2-x^2-12x+6-x\right)\)
\(=\left(3x+1\right)\left[\left(2x^3-x^2\right)+\left(2x^2-x\right)-\left(12x-6\right)\right]\)
\(=\left(3x+1\right)\left[x^2\left(2x-1\right)+x\left(2x-1\right)-6\left(2x-1\right)\right]\)
\(=\left(3x+1\right)\left(2x-1\right)\left(x^2+x-6\right)\)
\(=\left(3x+1\right)\left(2x-1\right)\left(x^2+3x-2x-6\right)\)
\(=\left(3x+1\right)\left(2x-1\right)\left[\left(x^2+3x\right)-\left(2x+6\right)\right]\)
\(=\left(3x+1\right)\left(2x-1\right)\left[x\left(x+3\right)-2\left(x+3\right)\right]\)
\(=\left(3x+1\right)\left(2x-1\right)\left(x+3\right)\left(x-2\right)\)
4 tháng 11 2017
1. \(x^4+6x^3+11x^2+6x+1\)
\(=\left(x^2\right)^2+2.x^2.3x+\left(3x\right)^2+2x^2+6x+1\)
\(=\left(x^2+3x\right)^2+2\left(x^2+3x\right)+1\)
\(=\left(x^2+3x+1\right)^2\)
3. \(x^4-7x^3+14x^2-7x+1\)
\(=x^2\left(x^2-7x+14-\dfrac{7}{x}+\dfrac{1}{x^2}\right)\)
\(=x^2\left[\left(x^2+\dfrac{1}{x^2}\right)-\left(7x+\dfrac{7}{x}\right)+14\right]\)
\(=x^2\left[\left(x+\dfrac{1}{x}\right)^2-7\left(x+\dfrac{1}{x}\right)+12\right]\)
\(=x^2\left[\left(x+\dfrac{1}{x}\right)^2-2\left(x+\dfrac{1}{x}\right).\dfrac{7}{2}+\dfrac{49}{4}-\dfrac{1}{4}\right]\)
\(=x^2\left[\left(x+\dfrac{1}{x}-\dfrac{7}{2}\right)^2-\dfrac{1}{4}\right]\)
\(=\left(x^2+1-\dfrac{7}{2}x\right)^2-\left(\dfrac{1}{2}x\right)^2\)
\(=\left(x^2-3x+1\right)\left(x^2-4x+1\right)\)
Có thể phân tích thành HĐT tiếp hoặc không.
17 tháng 8 2016
c)x12+x6+1
Lần lượt thêm và bớt x9; x3;x6 ta đc:
=x12+x9-x6-x9-x6-x3+x6+x3+1
=x6(x6+x3+1)-x3(x6+x3+1)+(x6+x3+1)
=(x6-x3+1)(x6+x3+1)
17 tháng 8 2016
b)x4-7x3-14x2-7x+1
=x4-3x3+x2-4x3+12x2-4x+x2-3x+1
=x2(x2-3x+1)-4x(x2-3x+1)+(x2-3x+1)
=(x2-4x+1)(x2-3x+1)
14 tháng 8 2022
a: \(=2x^3+x^2-2x^2-x+6x+3\)
\(=\left(2x+1\right)\left(x^2-x+3\right)\)
b: \(=x^3+x^2+4x^2+4x+4x+4\)
\(=\left(x+1\right)\left(x^2+4x+4\right)\)
\(=\left(x+1\right)\left(x+2\right)^2\)
c: \(=\left(x^2+7x+12\right)\left(x^2+7x+10\right)-24\)
\(=\left(x^2+7x\right)^2+22\left(x^2+7x\right)+96\)
\(=\left(x^2+7x+6\right)\left(x^2+7x+16\right)\)
\(=\left(x+1\right)\left(x+6\right)\left(x^2+7x+16\right)\)
đề yêu cầu gì thế bạn
phan tich da thuc thanh nhan tu