Solve (x-4)+(x^3-64)=

$$( x - 4 ) + ( x ^ { 3 } - 64 ) =$$

Factor

$$\left(x-4\right)\left(x^{2}+4x+17\right)$$

Solution Steps

Multiply and combine like terms.

$$x^{3}+x-68$$

By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term -68 and q divides the leading coefficient 1. One such root is 4. Factor the polynomial by dividing it by x-4. Polynomial x^{2}+4x+17 is not factored since it does not have any rational roots.

$$\left(x-4\right)\left(x^{2}+4x+17\right)$$

Evaluate

$$x^{3}+x-68$$

Solution Steps

Subtract 64 from -4 to get -68.

$$x-68+x^{3}$$