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Ta có:\(x^3-7x-6=\left(x^3-3x^2\right)+\left(3x^2-9x\right)+\left(2x-6\right)\)
\(=\left(x-3\right)\left(x^2+3x+2\right)=\left(x-3\right)\left(x^2+2x+x+2\right)\)
\(=\left(x-3\right)\left(x+2\right)\left(x+1\right)\)
=x3-x-6x-6
=(x3-x)-(6x-6)
=x(x2-1)-6(x-1)
=x(x-1)(x+1)-6(x-1)
=(x-1)(x2+1-6)
\(-x^2+7x-6=-x^2+6x+x-6=-x\left(x-6\right)+\left(x-6\right)=\left(1-x\right)\left(x-6\right)\)
\(x^3-7x-6=x^3+3x^2+2x-3x^2-9x-6\)
\(=x\left(x^2+3x+2\right)-3\left(x^2+3x+2\right)\)
\(=\left(x-3\right)\left(x^2+3x+2\right)\)
\(=\left(x-3\right)\left(x^2+2x+x+2\right)\)
\(=\left(x-3\right)\left[x\left(x+2\right)+\left(x+2\right)\right]\)
\(=\left(x-3\right)\left(x+1\right)\left(x+2\right)\)
x-3=0 x=3 | x+1=0 x=-1 | x+2=0 x=-2 |
x3-7x+6
=x3+3x2-3x2-9x+2x+6
=x2(x+3)-3x(x+3)+2(x+3)
=(x2-3x+2)(x+3)
=(x2-2x-x+2)(x+3)
=[x(x-2)-(x-2)](x+3)
=(x-1)(x-2)(x+3)
\(x^3-7x+6\)
\(=x^3-x-6x+6\)
\(=\left(x^3-x\right)-\left(6x+6\right)\)
\(=x.\left(x^2-1\right)-6.\left(x+1\right)\)
\(=x.\left(x+1\right)\left(x-1\right)-6.\left(x+1\right)\)
\(=\left(x+1\right).\left[x.\left(x-1\right)-6\right]\)
\(=\left(x+1\right)\left(x^2-x-6\right)\)
\(\times^2+7\times+12\)
\(=(\times^2+4\times)+\left(3\times+12\right)\)
\(=\times\left(\times+4\right)+3\left(\times+4\right)\)
\(=\left(\times+4\right)\left(\times+3\right)\)
\(x^2+7x+12=x^2+3x+4x+12\)
\(=x\left(x+3\right)+4\left(x+3\right)=\left(x+3\right)\left(x+4\right)\)
Ta có:\(x^2-4\)
\(=x^2-2^2\)
\(=\left(x-2\right)\left(x+2\right)\)
\(x^2-4\)
\(=x^2-2^2\)
\(=\left(x-2\right)\left(x+2\right)\)
\(x^2+7x+12\)
cách 1: \(=x^2+4x+3x+12\)
\(=x\left(x+4\right)+3\left(x+4\right)\)
\(=\left(x+4\right)\left(x+3\right)\)
cách 2: \(=x^2+3x+4x+12\)
\(=x\left(x+3\right)+4\left(x+3\right)\)
\(=\left(x+3\right)\left(x+4\right)\)
cách 3: \(=\left(x^2+7x+12,25\right)-0.25\)
\(=\left(x+3.5\right)^2-0.5^2\)
\(=\left(x+3.5+0.5\right)\left(x+3.5-0.5\right)\)
\(=\left(x+4\right)\left(x+3\right)\)
lấy đâu ra 8 cách vậy trời!!!!!!!!!!!!!!!
Cách 1:
\(x^2+7x+12\)
\(=\left(x^2+4x\right)+\left(3x+12\right)\)
\(=x\left(x+4\right)+3\left(x+4\right)\)
\(=\left(x+3\right)\left(x+4\right)\)
\(x^2+7x+6\)
\(=x^2+x+6x+6\)
\(=x\left(x+1\right)+6\left(x+1\right)\)
\(=\left(x+1\right).\left(x+6\right)\)
\(x^2+7x+6=\left(x-6\right)\left(x-1\right)\)
-_-