Use synthetic division to divide f(x) by x - k for the given value of k. Then express f(x) in the form f(x) = (x - k)q(x) + r for
the given value of k.
-$$f ( x ) = 3 x ^ { 5 } + 4 x ^ { 4 } + 2 x ^ { 2 } - 1 ; \quad k = - 2$$
A) $f ( x ) = ( x + 2 ) \left( 3 x ^ { 4 } - 2 x ^ { 3 } + 4 x ^ { 2 } + 6 \right) - 13$
B) $f ( x ) = ( x + 2 ) \left( 3 x ^ { 4 } + 2 x ^ { 3 } + 4 x ^ { 2 } + 8 x \right) - 15$
C) $f ( x ) = ( x + 2 ) \left( 3 x ^ { 4 } - 2 x ^ { 3 } + 4 x ^ { 2 } - 6 x + 12 \right) - 25$
D) $f ( x ) = ( x + 2 ) \left( 3 x ^ { 4 } - 2 x ^ { 3 } + 6 x ^ { 2 } - 12 \right) + 23$

Question

Quizplus · Accepted Answer

Using synthetic division with k = -2, the quotient is $3x^4 - 2x^3 + 4x^2 - 6x + 12$ and the remainder is -25.

Use Synthetic Division to Divide F(x) by X - K f(x)=3x5+4x4+2x2−1;k=−2f ( x ) = 3 x ^ { 5 } + 4 x ^ { 4 } + 2 x ^ { 2 } - 1 ; \quad k = - 2f(x)=3x5+4x4+2x2−1;k=−2

Use Synthetic Division to Divide F(x) by X - K $f ( x ) = 3 x ^ { 5 } + 4 x ^ { 4 } + 2 x ^ { 2 } - 1 ; \quad k = - 2$