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.
-$$f ( x ) = 3 x ^ { 4 } - 2 x ^ { 3 } - 10 x ^ { 2 } + 15 ; \quad k = 2$$
A) $f ( x ) = ( x - 2 ) \left( 3 x ^ { 3 } + 4 x ^ { 2 } - 2 x - 4 \right) + 7$
B) $f ( x ) = ( x - 2 ) \left( 3 x ^ { 3 } - 4 x ^ { 2 } - 2 x - 4 \right) + 7$
C) $f ( x ) = ( x - 2 ) \left( 3 x ^ { 3 } + 4 x ^ { 2 } + 2 x + 4 \right) + 22$
D) $f ( x ) = ( x - 2 ) \left( 3 x ^ { 3 } + 4 x ^ { 2 } - 2 x + 11 \right) + 22$

Question

Quizplus · Accepted Answer

Using synthetic division with $k = 2$, we divide $f(x) = 3x^4 - 2x^3 - 10x^2 + 15$ by $x - 2$. The coefficients of $f(x)$ are 3, -2, -10, 0, and 15 (note the 0 for the missing $x$ term). The synthetic division process yields a quotient of $3x^3 + 4x^2 - 2x - 4$ and a remainder of 7, thus $f(x) = (x - 2)(3x^3 + 4x^2 - 2x - 4) + 7$.

Use Synthetic Division to Divide F(x) by X - K f(x)=3x4−2x3−10x2+15;k=2f ( x ) = 3 x ^ { 4 } - 2 x ^ { 3 } - 10 x ^ { 2 } + 15 ; \quad k = 2f(x)=3x4−2x3−10x2+15;k=2

Use Synthetic Division to Divide F(x) by X - K $f ( x ) = 3 x ^ { 4 } - 2 x ^ { 3 } - 10 x ^ { 2 } + 15 ; \quad k = 2$