Evaluate
\frac{7+3x-x^{2}-x^{3}}{4}
Expand
\frac{7+3x-x^{2}-x^{3}}{4}
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\left(-x^{2}-2x-3\right)\left(\frac{1}{4}x-\frac{1}{4}\right)+x+1
To find the opposite of x^{2}+2x+3, find the opposite of each term.
-\frac{1}{4}x^{3}-\frac{1}{4}x^{2}-\frac{1}{4}x+\frac{3}{4}+x+1
Use the distributive property to multiply -x^{2}-2x-3 by \frac{1}{4}x-\frac{1}{4} and combine like terms.
-\frac{1}{4}x^{3}-\frac{1}{4}x^{2}+\frac{3}{4}x+\frac{3}{4}+1
Combine -\frac{1}{4}x and x to get \frac{3}{4}x.
-\frac{1}{4}x^{3}-\frac{1}{4}x^{2}+\frac{3}{4}x+\frac{7}{4}
Add \frac{3}{4} and 1 to get \frac{7}{4}.
\left(-x^{2}-2x-3\right)\left(\frac{1}{4}x-\frac{1}{4}\right)+x+1
To find the opposite of x^{2}+2x+3, find the opposite of each term.
-\frac{1}{4}x^{3}-\frac{1}{4}x^{2}-\frac{1}{4}x+\frac{3}{4}+x+1
Use the distributive property to multiply -x^{2}-2x-3 by \frac{1}{4}x-\frac{1}{4} and combine like terms.
-\frac{1}{4}x^{3}-\frac{1}{4}x^{2}+\frac{3}{4}x+\frac{3}{4}+1
Combine -\frac{1}{4}x and x to get \frac{3}{4}x.
-\frac{1}{4}x^{3}-\frac{1}{4}x^{2}+\frac{3}{4}x+\frac{7}{4}
Add \frac{3}{4} and 1 to get \frac{7}{4}.
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