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

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- Apr 7th 2009, 07:53 AMMr RayonThe remainder and factor theorems
The remainder when x^2 - 3x + 1 is divided by (x + d) is 11. Find the possible values of d.

- Apr 7th 2009, 08:22 AMstapel
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

. . . . .

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**.

(Wink) - Apr 7th 2009, 08:58 AMSoroban
Hello, Mr Rayon!

Quote:

The remainder when is divided by is 11.

Find the possible values of

. . If a polynomial is divided by , the remainder is

We have: .

When is divided by , the remainder is

We have: . divided by

Hence: .

Therefore: .

- Apr 7th 2009, 04:15 PMMr Rayon
- Apr 7th 2009, 04:29 PMmr fantastic
- Apr 7th 2009, 04:40 PMMr Rayon
- Apr 7th 2009, 04:41 PMstapel
- Apr 7th 2009, 04:45 PMMr Rayon