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.
-$$f ( x ) = x ^ { 5 } + x ^ { 2 } + 1 ; x - 2$$
A) $( x - 2 ) \left( x ^ { 4 } + 2 x ^ { 3 } + 4 x ^ { 2 } + 9 x + 18 \right) + 37$
B) $( x - 2 ) \left( x ^ { 4 } + 3 \right) + 7$
C) $( x - 2 ) \left( x ^ { 4 } + 3 x ^ { 2 } \right) + 7$
D) $( x - 2 ) \left( x ^ { 4 } + 2 x ^ { 3 } + 5 x ^ { 2 } + 10 x + 20 \right) + 41$

Question

Quizplus · Accepted Answer

Using synthetic division with $c = 2$, the coefficients of $f(x) = x^5 + 0x^4 + 0x^3 + x^2 + 0x + 1$ are divided by $x - 2$, resulting in a quotient of $x^4 + 2x^3 + 4x^2 + 8x + 18$ and a remainder of 37, thus confirming option A.

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