Solve 4xxx+x+5

$$4xxx+x+5$$

Evaluate

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

Solution Steps

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

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

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

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

Factor

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

Solution Steps

Multiply and combine like terms.

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

By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term 5 and q divides the leading coefficient 4. One such root is -1. Factor the polynomial by dividing it by x+1. Polynomial 4x^{2}-4x+5 is not factored since it does not have any rational roots.

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