True or False: -4 is a root \( \left(x\right. \)-int) of \( x^{3}-2 x^{2}+5 x+8 \)

To find out if -4 is a root of the polynomial \( x^{3}-2 x^{2}+5 x+8 \), we substitute \( x = -4 \) into the equation: \[ (-4)^3 - 2(-4)^2 + 5(-4) + 8 = -64 - 32 - 20 + 8 = -108 \] Since the result is not equal to zero, -4 is not a root of the polynomial. So the statement is false. As you can see, polynomial equations can sometimes lead to surprising results! When checking roots, plugging in values is the quickest way to confirm whether a candidate is actually a solution. The lesson here? Always double-check your calculations to avoid misjudgments, especially when playing with negative numbers, because they have a sneaky habit of throwing you off!