Solve -2x^{5}+3x^4+0x^3-5x^2-2x+1*quad3x^2+2x

$$- 2 x ^ { 5 } + 3 x ^ { 4 } + 0 x ^ { 3 } - 5 x ^ { 2 } - 2 x + 1 \times \quad 3 x ^ { 2 } + 2 x$$

Evaluate

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

Solution Steps

Anything times zero gives zero.

$$-2x^{5}+3x^{4}+0-5x^{2}-2x+1\times 3x^{2}+2x$$

Multiply 1 and 3 to get 3.

$$-2x^{5}+3x^{4}+0-5x^{2}-2x+3x^{2}+2x$$

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

$$-2x^{5}+3x^{4}+0-2x^{2}-2x+2x$$

Combine -2x and 2x to get 0.

$$-2x^{5}+3x^{4}+0-2x^{2}$$

Anything plus zero gives itself.

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

Factor

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

Solution Steps

Factor out x.

$$x\left(-2x^{4}+3x^{3}-2x\right)$$

Consider -2x^{4}+3x^{3}-5x-2+3x+2. Multiply and combine like terms.

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

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

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

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

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