{{ Form::open(array('action' =>('ProductController@postUseSearch'))) }}
    {{ Form::text('keyword', null, array('placeholder' => 'search by keyword')) }}
    {{ Form::submit('search') }}
{{ Form::close() }}

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Route::get('/search/', array(
    'as'    => 'name-search',
    'uses'  => 'ProductController@showSearchPage'
));

Route::post('/search/', array(
    'as'    => 'name-search-post',
    'uses'  => 'ProductController@postUseSearch'
));

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

   public function postUseSearch(){

        $searchString = Input::get('keyword');

        $insert                         = new Searchword();
        $insert->keyword                = $searchString; // not saving into the database?

more code...

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

<?php

use Illuminate\Auth\UserTrait;
use Illuminate\Auth\UserInterface;
use Illuminate\Auth\Reminders\RemindableTrait;
use Illuminate\Auth\Reminders\RemindableInterface;

class Searchword extends Eloquent implements UserInterface, RemindableInterface {

    protected $fillable = array (
        'keyword'
    );

    use UserTrait, RemindableTrait;

    /**
     * The database table used by the model.
     *
     * @var string
     */
    protected $table = 'searchword';

    /**
     * The attributes excluded from the model's JSON form.
     *
     * @var array
     */
    protected $hidden = array();

}

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Database Schema 
id (int) 
keyword (varchar 255) 
updated_at (datetime) 
created_at (datetime)