Use the remainder theorem and synthetic division to find f(k).
-$$\mathrm { k } = - 3 ; \mathrm { f } ( \mathrm { x } ) = 3 \mathrm { x } ^ { 3 } - 7 \mathrm { x } ^ { 2 } - 5 \mathrm { x } + 5$$
A) 48
B) $- 124$
C) $- 38$
D) $- 154$

Question

Quizplus · Accepted Answer

To use the remainder theorem and synthetic division to find $f(k)$ for $k = -3$, we set up synthetic division with $-3$ and the coefficients of $f(x) = 3x^3 - 7x^2 - 5x + 5$. The process is as follows:-3 | 3  -7  -5  5       ----  9  -6  33       ----------------         3   2   4  38However, since $k = -3$, we should correct the synthetic division process to reflect the correct calculation:-3 | 3  -7  -5  5       ----  -9  48  -129       ----------------         3  -16  43  -124The remainder, which is the value of $f(k)$ when $k = -3$, is $-124$. Therefore, the correct answer is $-124$.

Use the Remainder Theorem and Synthetic Division to Find F(k) k=−3;f(x)=3x3−7x2−5x+5\mathrm { k } = - 3 ; \mathrm { f } ( \mathrm { x } ) = 3 \mathrm { x } ^ { 3 } - 7 \mathrm { x } ^ { 2 } - 5 \mathrm { x } + 5k=−3;f(x)=3x3−7x2−5x+5

Use the Remainder Theorem and Synthetic Division to Find F(k) $\mathrm { k } = - 3 ; \mathrm { f } ( \mathrm { x } ) = 3 \mathrm { x } ^ { 3 } - 7 \mathrm { x } ^ { 2 } - 5 \mathrm { x } + 5$