Solve x^3-343-x+7

$$x ^ { 3 } - 343 - x + 7$$

Factor

$$\left(x-7\right)\left(x^{2}+7x+48\right)$$

Solution Steps

Multiply and combine like terms.

$$x^{3}-x-336$$

By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term -336 and q divides the leading coefficient 1. One such root is 7. Factor the polynomial by dividing it by x-7. Polynomial x^{2}+7x+48 is not factored since it does not have any rational roots.

$$\left(x-7\right)\left(x^{2}+7x+48\right)$$

Evaluate

$$x^{3}-x-336$$

Solution Steps

Add -343 and 7 to get -336.

$$x^{3}-336-x$$