Phân tích các đa thức sau thành nhân tử:
a) x3 = 2x2 + x
b) 2x2 + 4x + 2 -2y2
c) 2xy - x2 - y2 + 16
Phân tích các đa thức sau thành nhân tử
a) x2 - 3x +2
b) x2 + x - 6
c) x2 + 5x + 6
Phân tích các đa thức sau thành nhân tử:
a) x3 + 2x2y + xy2 - 9x
b) 2x - 2y - x2 + 2xy - y2
c) x4 - 2x2
Phân tích các đa thức sau thành nhân tử:
a) x2 - 4x + 3
b) x2 + 5x + 4
c) x2 - x - 6
d) x4 + 4
\(a)x^3+2x^2+x\)
\(=x\left(x^2+2x+1\right)\)
\(=x\left(x+1\right)^2\)
\(b)2x^2+4x+2-2y^2\)
\(=2\left(x^2+2x+1-y^2\right)\)
\(=2\left[\left(x^2+2x+1\right)-y^2\right]\)
\(=2\left[\left(x+1\right)^2-y^2\right]\)
\(=2\left(x+1-y\right)\left(x+1+y\right)\)
\(c)2xy-x^2-y^2+16\)
\(=16-\left(-2xy+x^2+y^2\right)\)
\(=4^2-\left(x-y\right)^2\)
\(=\left(4-x+y\right)\left(4+x-y\right)\)
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\(a)x^2-3x+2\)
\(=x^2-x-2x+2\)
\(=x\left(x-1\right)-2\left(x-1\right)\)
\(=\left(x-1\right)\left(x-2\right)\)
\(b)x^2+x-6\)
\(=x^2-2x+3x-6\)
\(=x\left(x-2\right)+3\left(x-2\right)\)
\(=\left(x-2\right)\left(x+3\right)\)
\(c)x^2+5x+6\)
\(=x^2+2x+3x+6\)
\(=x\left(x+2\right)+3\left(x+2\right)\)
\(=\left(x+2\right)\left(x+3\right)\)
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\(a)x^3+2x^2y+xy^2-9x\)
\(=x\left(x^2+2xy+y^2-9\right)\)
\(=x\left[\left(x^2+2xy+y^2\right)-9\right]\)
\(=x\left[\left(x+y\right)^2-3^2\right]\)
\(=x\left(x+y-3\right)\left(x+y+3\right)\)
\(b)2x-2y-x^2+2xy-y^2\)
\(=2\left(x-y\right)-\left(x^2-2xy+y^2\right)\)
\(=2\left(x-y\right)-\left(x-y\right)^2\)
\(=\left(2-x+y\right)\left(x-y\right)\)
\(c)x^4-2x^2\)
\(=x^4-2x^2+1-1\)
\(=\left(x^2-1\right)^2-1\)
\(=x^2\left(x^2-2\right)\)
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\(a)x^2-4x+3\)
\(=x^2-x-3x+3\)
\(=\left(x^2-x\right)-\left(3x-3\right)\)
\(=x\left(x-1\right)-3\left(x-1\right)\)
\(=\left(x-1\right)\left(x-3\right)\)
\(b)x^2+5x+4\)
\(=x^2+x+4x+4\)
\(=\left(x^2+x\right)+\left(4x+4\right)\)
\(=x\left(x+1\right)+4\left(x+1\right)\)
\(=\left(x+1\right)\left(x+4\right)\)
\(c)x^2-x-6\)
\(=x^2+2x-3x-6\)
\(=\left(x^2+2x\right)-\left(3x+6\right)\)
\(=x\left(x+2\right)-3\left(x+2\right)\)
\(=\left(x+2\right)\left(x-3\right)\)
\(d)x^4+4\)
\(=\left(x^2\right)^2+4\)
\(=\left(x^2\right)^2+2x^2.2+4-2x^2.2\)
\(=\left[\left(x^2\right)^2+2x^2.2+4\right]-\left(2x\right)^2\)
\(=\left(x^2+2\right)^2-\left(2x\right)^2\)
\(=\left(x^2+2-2x\right)\left(x^2+2+2x\right)\)