Solve the problem.
-Use synthetic division to divide $f ( x ) = x ^ { 3 } - 10 x ^ { 2 } + 19 x + 30$ by $x - 6$. Use the result to find all zeros of $f$.
A) $\{ 6,5 , - 1 \}$
B) $\{ 6 , - 5,1 \}$
C) $\{ - 6 , - 5,1 \}$
D) $\{ - 6,5 , - 1 \}$

Question

Quizplus · Accepted Answer

Using synthetic division with $x - 6$, the coefficients of $f(x)$ become $1, -10, 19, 30$. Dividing by 6, the remainder is 0, indicating 6 is a zero. The resulting polynomial is $x^2 - 4x + 1$, which factors to $(x-5)(x+1)$, giving zeros at $x = 5$ and $x = -1$. Thus, the zeros of $f(x)$ are $\{6, 5, -1\}$.

Solve the Problem f(x)=x3−10x2+19x+30f ( x ) = x ^ { 3 } - 10 x ^ { 2 } + 19 x + 30f(x)=x3−10x2+19x+30

Solve the Problem $f ( x ) = x ^ { 3 } - 10 x ^ { 2 } + 19 x + 30$