Evaluate
\left(x-1\right)\left(8+10x-x^{2}\right)
Factor
\left(x-1\right)\left(8+10x-x^{2}\right)
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-x^{3}+11x^{2}-5x+3x-8
Combine 3x^{2} and 8x^{2} to get 11x^{2}.
-x^{3}+11x^{2}-2x-8
Combine -5x and 3x to get -2x.
-x^{3}+11x^{2}-2x-8
Multiply and combine like terms.
\left(x-1\right)\left(-x^{2}+10x+8\right)
By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term -8 and q divides the leading coefficient -1. One such root is 1. Factor the polynomial by dividing it by x-1. Polynomial -x^{2}+10x+8 is not factored since it does not have any rational roots.
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\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
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Limits
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