How to use synthetic division to divide f(x) by x-c then write f(x) in the form....

f(x)=(x-c)q(x)+r

for f(x)=2x^3+5x+2;x-3

f(x)=

First, determine the test zero, which is 3. Then, set up the corresponding coefficients of 2x³ + 5x + 2 [2x³ + 0x² + 5x + 2]. Evaluate.

3 | 2 + 0 . + 5 .+ 2
. . . + 6 + 18 + 69
. . 2 + 6 + 23 + 71

Therefore, we obtain f(x) = (2x² + 6x + 23)(x - 3) + 71

I hope this helps!