WEBVTT

1
00:00:00.000 --> 00:00:03.820
Here is the problem: x squared minus 4x plus 3.

2
00:00:04.270 --> 00:00:06.975
Factor a polynomial over the rational numbers.

3
00:00:07.775 --> 00:00:10.085
Write the polynomial in standard form.

4
00:00:10.535 --> 00:00:24.130
Use the AC method. Multiply a times c equals 1 times 3 equals 3. Find two numbers whose product is 3 and whose sum is b equals negative 4: negative 1 and negative 3.

5
00:00:24.580 --> 00:00:33.427
Factor by grouping. Group the first two and last two terms, factor each group, then factor out the common binomial. The roots are 1 and 3.

6
00:00:33.877 --> 00:00:35.572
Write the complete factorization.

7
00:00:36.372 --> 00:00:39.681
So the answer is (x minus 3)(x minus 1).

8
00:00:40.131 --> 00:00:47.143
x squared minus 4x plus 3 factors completely over the rationals as (x minus 3)(x minus 1).

9
00:00:47.943 --> 00:00:54.166
Expanding (x minus 3)(x minus 1) gives back x squared minus 4x plus 3.