AngularJs ~1.6 pass parameter using ng-pattern to factory

Question

Is it possible to pass a parameter from ng-pattern(html input) to AngularJs factory? At the moment, I have a custom factory validateFormFieldFactory. And the custom factory/service is going to be injected for each controller with form.

var app = angular.module('app', []);

// // I would like to have something like this
//  app.factory('validateFormFieldFactory', function(fieldType) {
app.factory('validateFormFieldFactory', function() {
  var objRegExp = {
    "firstName": /^[a-zA-Z]*-*$/,
    "lastName": /^[1-9]*-*$/,
    "eMail": /^[a-z]*-*$/
  };
  
  var regexp = /^[a-zA-Z]*-*$/;
  // I would like to have something like this
  //var regexp = objRegExp[fieldType]; // fx, first name, last name, email and so on

  return {
    test: function(value) {
      return regexp.test(value);
    }
  };
});

app.controller('CalculatorController', function($scope, validateFormFieldFactory) {

  $scope.validateFormFieldFactory = validateFormFieldFactory;
});

<script src="https://ajax.googleapis.com/ajax/libs/angularjs/1.6.7/angular.min.js"></script>


<div ng-app="app">
  <div ng-controller="CalculatorController">
    Enter a something:
    <input type="url" 
           class="form-control" 
           name="pt-test" 
           ng-model="Website" 
           ng-maxlength="50"
           ng-pattern="validateFormFieldFactory"/>
           <!-- // I would like to have something like this -->
           <!--ng-pattern="validateFormFieldFactory('firstName')" -->
           
  </div>
</div>

The idea is to use the factory for the whole application(reusable factory). It can be a factory, service, provider or directive. At the moment I haven't found any example how to do this kind of magic, but it would be really helpful if I could just specify firstName, LastName or email and so on using ng-pattern and the service. Something like this maybe helps - Example2