Use the remainder theorem and synthetic division to find f(k).
-$k = - 3 ; f ( x ) = 3 x ^ { 4 } + 5 x ^ { 3 } + 6 x ^ { 2 } - 6 x + 24$
A) 204
B) 360
C) $- 444$
D) 282

Question

Quizplus · Accepted Answer

Using the remainder theorem, when we substitute $k = -3$ into $f(x)$, we get $f(-3) = 3(-3)^4 + 5(-3)^3 + 6(-3)^2 - 6(-3) + 24$. Calculating this gives $f(-3) = 3(81) - 5(27) + 6(9) + 18 + 24 = 243 - 135 + 54 + 18 + 24 = 204$.

Use the Remainder Theorem and Synthetic Division to Find F(k) k=−3;f(x)=3x4+5x3+6x2−6x+24k = - 3 ; f ( x ) = 3 x ^ { 4 } + 5 x ^ { 3 } + 6 x ^ { 2 } - 6 x + 24k=−3;f(x)=3x4+5x3+6x2−6x+24

Use the Remainder Theorem and Synthetic Division to Find F(k) $k = - 3 ; f ( x ) = 3 x ^ { 4 } + 5 x ^ { 3 } + 6 x ^ { 2 } - 6 x + 24$