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\(B=x^4+3x^3-x^2+3x^3+9x^2-3x-x^2-3x+1\)
\(=\left(x^2+3x-1\right)^2\)
Bài này ko thể phân tích theo kiểu lớp 8 được (chưa học căn thức)
\(2x^2-6x+1=\left(\sqrt{2}x\right)^2-2.\sqrt{2}x.\frac{3\sqrt{2}}{2}+\left(\frac{3\sqrt{2}}{2}\right)^2-\frac{7}{2}\)
\(=\left(\sqrt{2}x-\frac{3\sqrt{2}}{2}\right)^2-\left(\frac{\sqrt{14}}{2}\right)^2\)
\(=\left(\sqrt{2}x-\frac{3\sqrt{2}}{2}+\frac{\sqrt{14}}{2}\right)\left(\sqrt{2}x-\frac{3\sqrt{2}}{2}-\frac{\sqrt{14}}{2}\right)\)
\(=\left(\sqrt{2}x+\frac{\sqrt{14}-3\sqrt{2}}{2}\right)\left(\sqrt{2}x-\frac{\sqrt{14}+3\sqrt{2}}{2}\right)\)
\(2x^2-6x+1=2\left(x^2-3x+\frac{9}{4}-\frac{7}{4}\right)=2\left[\left(x-\frac{3}{2}\right)^2-\left(\frac{\sqrt{7}}{2}\right)^2\right]=2\left(x-\frac{3}{2}-\frac{\sqrt{7}}{2}\right)\left(x-\frac{3}{2}+\frac{\sqrt{7}}{2}\right)\)
\(=2\left(x-\frac{3+\sqrt{7}}{2}\right)\left(x-\frac{3-\sqrt{7}}{2}\right)\)
\(=6x^2-2x-\left(9x-3\right)\)
\(=2x\left(3x-1\right)-3\left(3x-1\right)\)
\(=\left(2x-3\right)\left(3x-1\right)\)
$ 2x^3 - x^2 + 5x + 3 \\ = 2x^3 + x^2 - 2x^2 - x + 6x + 3 \\ = x^2(2x + 1) - x(2x + 1) + 3(2x + 1) \\ = (2x + 1)(x^2 - x + 3) $
\(2x^3-x^2+5x+3\)
= \(2x^3+x^2-2x^2-x+6x+3\)
\(=x^2\left(2x+1\right)-x\left(2x+1\right)+3\left(2x+1\right)\)
\(=\left(2x+1\right)\left(x^2-x+3\right)\)
Vì \(x^2-x+3=\left(x-\dfrac{1}{2}\right)^2-\dfrac{1}{4}+3>0\)
Nên
\(2x^3-x^2+5x+3=\left(2x+1\right)\left(x^2-x+3\right)\)
câu 1:
x3-1+3x2-3x =(x-1)(x^2+x+1)+3x(x-1)=(x-1)(x^2+x+1+3x)=(x-1)(x^2+4x=1)
Câu 2 :
a) \(\left(x^4-2x^3+2x-1\right):\left(x^2-1\right)\)
\(=\left(x^4-x^2-2x^3+2x+x^2-1\right):\left(x^2-1\right)\)
\(=\left[x^2\left(x^2-1\right)-2x\left(x^2-1\right)+\left(x^2-1\right)\right]:\left(x^2-1\right)\)
\(=\left(x^2-1\right)\left(x^2-2x+1\right):\left(x^2-1\right)\)
\(=x^2-2x+1\)
b) \(\left(x^6-2x^5+2x^4+6x^3-4x^2\right):6x^2\)
\(=\frac{1}{6}x^4-\frac{1}{3}x^3+\frac{1}{3}x^2+x-\frac{2}{3}\)
Câu 3 :
Sửa đề :
\(\frac{3x^2+6x+12}{x^3-8}=\frac{3\left(x^2+2x+4\right)}{\left(x-2\right)\left(x^2+2x+4\right)}=\frac{3}{x-2}\)
a, = 2 x 2 - 6x +9x - 27
=(x-3).2x +9.(x-3)
=(x-3).(2x+9)
b, = 2x2-6xy+xy -3y2
= 2x.(x-3y) +y.(x-3y)
= (x-3y).(2x+y)
a) x^3 +5x^2+6x
= x^3+2x^2+3x^2+6x
=x*(x+3)*(x+2)
b) x^2-6x+8
= x^2-2x-4x+8
=(x-2)*(x-4)
c)2x^2+98+28x-8y^2
=2(x^2+14x+49-4y^2)
=2*[(x+7)^2-4y^2]
2*(x-7-2y)*(x-7+2y)
a) x2 + 2x2 + 3x2 + 6x
= x( x+2 ) + 3( x+2 )
=(x+3)(x+2)
b) x2 - 2x - 4x + 8
=x(x-2)-4(x-2)
=(x-4)(x-2)
c)