Clase para creación de un captcha matemático

<?php
/**
 * Captcha
 * -------------------------------------
 *
 * @author iBet7o - <[email protected]>
 */
class Captcha
{
    private $_operations = array('+', '-', '*');

    private $_question = array();

    public $answer = NULL;

    private function _operation()
    {
        $this->_question[] = rand(1, 20);
        $this->_question[] = $this->_operations[rand(0, 2)];
        $this->_question[] = rand(1, 20);

        $cal = $this->_question[0];
        if($this->_question[1] == '+')
        {
            $cal += $this->_question[2];
        }
        elseif($this->_question[1] == '-')
        {
            $cal -= $this->_question[2];
        }
        elseif($this->_question[1] == '*')
        {
            $cal *= $this->_question[2];
        }

        $this->_question = implode(' ', $this->_question);
        $this->answer = $cal;
    }

    private function _image()
    {
        header("Content-type: image/png");

        $image = @imagecreate(8 * strlen($this->_question), 15);

        $background_color = imagecolorallocate($image, 255, 255, 255);

        $color = imagecolorallocate($image, 0, 0, 0);

        imagestring($image, 4, 0, 0,  $this->_question, $color);

        imagepng($image);
        imagedestroy($image);
    }

    public function show()
    {
        $this->_operation();
        $this->_image();
    }
}