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6x^{2}-2\times 3x+12
Multiply 3 and 2 to get 6.
6x^{2}-6x+12
Multiply 2 and 3 to get 6.
6\left(x^{2}-x+2\right)
Factor out 6. Polynomial x^{2}-x+2 is not factored since it does not have any rational roots.