Use synthetic division to decide whether the given number k is a zero of the given polynomial function.
-$k = \frac { 2 } { 3 } ; f ( x ) = 3 x ^ { 4 } + 5 x ^ { 2 } + 2$

Question

Quizplus · Accepted Answer

Synthetic division can be used to test if a rational number is a zero of a polynomial, but in this case, since the polynomial $f(x) = 3x^4 + 5x^2 + 2$ does not have a term for every power of x down to the constant term, when setting up the synthetic division, you must include terms for $x^3$ and $x^1$ with coefficients of 0. The correct setup for synthetic division should account for all powers of x, even those with coefficients of 0, to accurately determine if $k = \frac{2}{3}$ is a zero.

Use Synthetic Division to Decide Whether the Given Number K k=23;f(x)=3x4+5x2+2k = \frac { 2 } { 3 } ; f ( x ) = 3 x ^ { 4 } + 5 x ^ { 2 } + 2k=32​;f(x)=3x4+5x2+2

Use Synthetic Division to Decide Whether the Given Number K $k = \frac { 2 } { 3 } ; f ( x ) = 3 x ^ { 4 } + 5 x ^ { 2 } + 2$