SAT Mathematics Practice Test 4

The four-term polynomial expression can be factored completely, by grouping, as follows:$\left({\mathit{x}}^3-5{\mathit{x}}^2\right)+\left(2\mathit{x}-10\right)=0$
${\mathit{x}}^2\left(\mathit{x}-5\right)+2\left(\mathit{x}-5\right)=0$
$\left(\mathit{x}-5\right)\left(\mathit{x}+2\right)=0$By the zero product property, set each factor of the polynomial equal to 0 and solve each resulting equation for $\mathit{x}$. This gives $\mathit{x}=5$ or $\mathit{x}=\pm \mathit{i}\sqrt{2}$,respectively.Because the question asks for the real value of x that satisfies the equation, the correct answer is 5.