WEBVTT

1
00:00:00.000 --> 00:00:03.158
Here is the problem: x squared minus 2.

2
00:00:03.608 --> 00:00:06.313
Factor a polynomial over the rational numbers.

3
00:00:07.113 --> 00:00:09.505
Write the polynomial in standard form.

4
00:00:09.955 --> 00:00:19.464
Check the discriminant. b squared minus 4ac equals 8. It is not a perfect square, so the quadratic does not factor over the rational numbers.

5
00:00:19.914 --> 00:00:22.793
The polynomial is prime over the rationals.

6
00:00:23.593 --> 00:00:26.182
So the answer is x squared minus 2.

7
00:00:26.632 --> 00:00:34.829
x squared minus 2 has no factors with rational coefficients other than constants, so it is already fully factored over the rationals.

8
00:00:35.629 --> 00:00:40.354
Expanding x squared minus 2 gives back x squared minus 2.