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# Use synthetic division to show that x is a solution of the thirddegree polynomial equation, and use the result to factor the polynomial completely. List all the real solutions of the equation. Polynomial Equation $2 x^{3}-17 x^{2}+12 x+63=0$ Value of x $x=-\frac{3}{2}$

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In order to prove that our value of $x$ is a solution of the third-degree polynomial equation using synthetic division, we need to find the remainder of the division of our polynomial equation divided by the factor $(x-k)$ where $k$ is our $x$ value:

• If the remainder of the synthetic division is $0$, the $x$ is a sollution of the polynomial equation.

• If the remainder of the synthetic division is not $0$, the $x$ is not a sollution of the polynomial equation.

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