Originally Posted by

**Mr Rayon** The remainder when x^2 - 3x + 1 is divided by (x + d) is 11. Find the possible values of d.

Since the divisor is x + d, then the zero (when doing the **synthetic division**) is -d. So do the synthetic division:

Code:

-d | 1 -3 1
| -d d^2+3d
+------------------
1 -d-3 d^2+3d+1

Set the remainder equal to the given value:

. . . . .

This rearranges as:

. . . . .

Either **factor the quadratic** and then solve the factors for the values of d, or else plug the above into **the Quadratic Formula**.