How to override function widget in default-widgets.php

Hello,

I wonder how I can override the function widget in the file default-widget.php on lines 377-386 from the functions.php file in the themes folder?

377-386

function widget( $args, $instance ) {
		extract($args);
		$title = apply_filters( 'widget_title', empty($instance['title']) ? '' : $instance['title'], $instance, $this->id_base);
		$text = apply_filters( 'widget_text', $instance['text'], $instance );
		echo $before_widget;
		if ( !empty( $title ) ) { echo $before_title . $title . $after_title; } ?>
			<div class="textwidget"><?php echo $instance['filter'] ? wpautop($text) : $text; ?></div>
		<?php
		echo $after_widget;
	}

I have found that you should be able to override with the code (this is a snippet i found, its need to be modified, but Im not sure how):

function twentyten_remove_recent_comments_style() {
	global $wp_widget_factory;
	remove_action( 'wp_head', array( $wp_widget_factory->widgets['WP_Widget_Text'], 'recent_comments_style' ) );
}
add_action( 'widgets_init', 'twentyten_remove_recent_comments_style' );