Solve 4x^2+7x+x-2x^3+x-2x^3x^2-2x

$$4 x ^ { 2 } + 7 x + x - 2 x ^ { 3 } + x - 2 x ^ { 3 } x ^ { 2 } - 2 x$$

Evaluate

$$x\left(7+4x-2x^{2}-2x^{4}\right)$$

Solution Steps

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

$$4x^{2}+7x+x-2x^{3}+x-2x^{5}-2x$$

Combine 7x and x to get 8x.

$$4x^{2}+8x-2x^{3}+x-2x^{5}-2x$$

Combine 8x and x to get 9x.

$$4x^{2}+9x-2x^{3}-2x^{5}-2x$$

Combine 9x and -2x to get 7x.

$$4x^{2}+7x-2x^{3}-2x^{5}$$

Factor

$$x\left(7+4x-2x^{2}-2x^{4}\right)$$

Solution Steps

Factor out x. Polynomial -2x^{4}-2x^{2}+4x+7 is not factored since it does not have any rational roots.

$$x\left(4x+7-2x^{2}x^{2}-2x^{2}\right)$$