Solve 5x^5+4(left(x^2right)^2)+3xxx+2x^2+x

$$5 { x }^{ 5 } +4( { \left( { x }^{ 2 } \right) }^{ 2 } )+3xxx+2 { x }^{ 2 } +x$$

Evaluate

$$x\left(5x^{4}+4x^{3}+3x^{2}+2x+1\right)$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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

Multiply x and x to get x^{2}.

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

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

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

Factor

$$x\left(5x^{4}+4x^{3}+3x^{2}+2x+1\right)$$

Solution Steps

Factor out common term x by using distributive property.

$$x\left(5x^{4}+4x^{3}+3xx+2x+1\right)$$

Consider 5x^{4}+4x^{3}+3xx+2x+1. Simplify.

$$5x^{4}+4x^{3}+3x^{2}+2x+1$$

Rewrite the complete factored expression. Polynomial 5x^{4}+4x^{3}+3x^{2}+2x+1 is not factored since it does not have any rational roots.

$$x\left(5x^{4}+4x^{3}+3x^{2}+2x+1\right)$$