ParallaxBackground.cs

using UnityEngine;
using System.Collections;

public class ParallaxBackground : MonoBehaviour
{
  public Vector2 ParallaxFactor;

  public Camera MainCamera;

  private Vector2 lastPos;

    // Use this for initialization
    void Start ()
  {
    lastPos = MainCamera.transform.position;
    }

    // Update is called once per frame
    void Update ()
  {
    Vector2 newPos = MainCamera.transform.position;
    Vector2 diff = newPos - lastPos;

    transform.position += new Vector3(diff.x * ParallaxFactor.x, diff.y * ParallaxFactor.y);
    lastPos = newPos;
    }
}