Evaluate
4x^{3}-2x-\frac{33}{4}
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4x^{3}-2x-\frac{33}{4}
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\left(2x^{2}+3x+\frac{6+1}{2}\right)\left(2x-3\right)+\frac{2\times 4+1}{4}
Multiply 3 and 2 to get 6.
\left(2x^{2}+3x+\frac{7}{2}\right)\left(2x-3\right)+\frac{2\times 4+1}{4}
Add 6 and 1 to get 7.
\left(2x^{2}+3x+\frac{7}{2}\right)\left(2x-3\right)+\frac{8+1}{4}
Multiply 2 and 4 to get 8.
\left(2x^{2}+3x+\frac{7}{2}\right)\left(2x-3\right)+\frac{9}{4}
Add 8 and 1 to get 9.
4x^{3}-2x-\frac{21}{2}+\frac{9}{4}
Use the distributive property to multiply 2x^{2}+3x+\frac{7}{2} by 2x-3 and combine like terms.
4x^{3}-2x-\frac{33}{4}
Add -\frac{21}{2} and \frac{9}{4} to get -\frac{33}{4}.
\left(2x^{2}+3x+\frac{6+1}{2}\right)\left(2x-3\right)+\frac{2\times 4+1}{4}
Multiply 3 and 2 to get 6.
\left(2x^{2}+3x+\frac{7}{2}\right)\left(2x-3\right)+\frac{2\times 4+1}{4}
Add 6 and 1 to get 7.
\left(2x^{2}+3x+\frac{7}{2}\right)\left(2x-3\right)+\frac{8+1}{4}
Multiply 2 and 4 to get 8.
\left(2x^{2}+3x+\frac{7}{2}\right)\left(2x-3\right)+\frac{9}{4}
Add 8 and 1 to get 9.
4x^{3}-2x-\frac{21}{2}+\frac{9}{4}
Use the distributive property to multiply 2x^{2}+3x+\frac{7}{2} by 2x-3 and combine like terms.
4x^{3}-2x-\frac{33}{4}
Add -\frac{21}{2} and \frac{9}{4} to get -\frac{33}{4}.
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