Solve x^9:x^4-2x*x^4-x^3

$$x ^ { 9 } : x ^ { 4 } - 2 x \cdot x ^ { 4 } - x ^ { 3 }$$

Evaluate

$$-\left(x^{2}+1\right)x^{3}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 9 to get 5.

$$x^{5}-2xx^{4}-x^{3}$$

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$x^{5}-2x^{5}-x^{3}$$

Combine x^{5} and -2x^{5} to get -x^{5}.

$$-x^{5}-x^{3}$$

Factor

$$-\left(x^{2}+1\right)x^{3}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 9 to get 5.

$$factor(x^{5}-2xx^{4}-x^{3})$$

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$factor(x^{5}-2x^{5}-x^{3})$$

Combine x^{5} and -2x^{5} to get -x^{5}.

$$factor(-x^{5}-x^{3})$$

Factor out x^{3}. Polynomial -x^{2}-1 is not factored since it does not have any rational roots.

$$x^{3}\left(-x^{2}-1\right)$$