Use synthetic division to divide f(x)by x - c, and then write f(x)in the form f(x)= (x - c)q(x)+ r.
-$$f ( x ) = x ^ { 5 } - 3 x ^ { 4 } - 7 x ^ { 3 } - 12 x ^ { 2 } - 13 x - 7 ; x - 5$$
A) $( x - 5 ) \left( x ^ { 4 } + 2 x ^ { 3 } + 3 x ^ { 2 } + 3 x + 2 \right) + 3$
B) $( x - 5 ) \left( x ^ { 4 } + 2 x ^ { 3 } + 3 x ^ { 2 } + 3 x + 3 \right) + 0$
C) $( x - 5 ) \left( x ^ { 3 } + 2 x ^ { 2 } + 3 x + 3 \right) + 3$
D) $( x - 5 ) \left( x ^ { 4 } + 2 x ^ { 3 } + 3 x ^ { 2 } + 3 x - 2 \right) + 5$

Question

Quizplus · Accepted Answer

Using synthetic division with $c = 5$, the coefficients of $f(x)$ after division are $1, 2, 3, 3, 2$ with a remainder of $3$, fitting the form $(x - 5)(x^4 + 2x^3 + 3x^2 + 3x + 2) + 3$.

Use Synthetic Division to Divide F(x)by X - C, and Then