Question

Synthetic division for x^2+10x+21/x+3

Answer 1

X^2+10x+21/x+3?  If you meant (x^2+10x+21)/(x+3), please note that those parentheses are essential.

If you wish to divide x^2+10x+21 by (x+3) using synth. div., use the divisor -3:
 
                                        _______________
                                   -3 /    1      10      21  
                                                     -3      -21
                                         -----------------------
                                              1       7        0

Since the remainder is 0, (x+3) is a divisor of x^2+10x+21, and the other factor is (1x + 7).