Evaluate
-x^{3}+\frac{5x^{2}}{3}-12x+1
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-x^{3}+\frac{5x^{2}}{3}-12x+1
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3x^{2}-12x+3-\frac{1}{3}\left(3x^{3}+4x^{2}+6\right)
Use the distributive property to multiply 3 by x^{2}-4x+1.
3x^{2}-12x+3-x^{3}-\frac{4}{3}x^{2}-2
Use the distributive property to multiply -\frac{1}{3} by 3x^{3}+4x^{2}+6.
\frac{5}{3}x^{2}-12x+3-x^{3}-2
Combine 3x^{2} and -\frac{4}{3}x^{2} to get \frac{5}{3}x^{2}.
\frac{5}{3}x^{2}-12x+1-x^{3}
Subtract 2 from 3 to get 1.
3x^{2}-12x+3-\frac{1}{3}\left(3x^{3}+4x^{2}+6\right)
Use the distributive property to multiply 3 by x^{2}-4x+1.
3x^{2}-12x+3-x^{3}-\frac{4}{3}x^{2}-2
Use the distributive property to multiply -\frac{1}{3} by 3x^{3}+4x^{2}+6.
\frac{5}{3}x^{2}-12x+3-x^{3}-2
Combine 3x^{2} and -\frac{4}{3}x^{2} to get \frac{5}{3}x^{2}.
\frac{5}{3}x^{2}-12x+1-x^{3}
Subtract 2 from 3 to get 1.
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