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2x^{3}-6x+\left(x-2\right)\left(x^{2}-5x+1\right)
Use the distributive property to multiply 2x by x^{2}-3.
2x^{3}-6x+x^{3}-7x^{2}+11x-2
Use the distributive property to multiply x-2 by x^{2}-5x+1 and combine like terms.
3x^{3}-6x-7x^{2}+11x-2
Combine 2x^{3} and x^{3} to get 3x^{3}.
3x^{3}+5x-7x^{2}-2
Combine -6x and 11x to get 5x.
2x^{3}-6x+\left(x-2\right)\left(x^{2}-5x+1\right)
Use the distributive property to multiply 2x by x^{2}-3.
2x^{3}-6x+x^{3}-7x^{2}+11x-2
Use the distributive property to multiply x-2 by x^{2}-5x+1 and combine like terms.
3x^{3}-6x-7x^{2}+11x-2
Combine 2x^{3} and x^{3} to get 3x^{3}.
3x^{3}+5x-7x^{2}-2
Combine -6x and 11x to get 5x.