Solve 3xx^{4}+3xx^3-5x^2x^3-5x^2x=

$$3 x x ^ { 4 } + 3 x x ^ { 3 } - 5 x ^ { 2 } x ^ { 3 } - 5 x ^ { 2 } x =$$

Evaluate

$$\left(-2x^{2}+3x-5\right)x^{3}$$

Solution Steps

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

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

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

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

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

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

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$3x^{5}+3x^{4}-5x^{5}-5x^{3}$$

Combine 3x^{5} and -5x^{5} to get -2x^{5}.

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

Factor

$$\left(-2x^{2}+3x-5\right)x^{3}$$

Solution Steps

Factor out x.

$$x\left(3x^{4}+3x^{3}-5xx^{3}-5xx\right)$$

Consider 3x^{4}+3x^{3}-5x^{4}-5x^{2}. Factor out x^{2}.

$$x^{2}\left(3x^{2}+3x-5x^{2}-5\right)$$

Rewrite the complete factored expression. Polynomial -2x^{2}+3x-5 is not factored since it does not have any rational roots.

$$xx^{2}\left(-2x^{2}+3x-5\right)$$