WEBVTT

1
00:00:00.000 --> 00:00:04.180
Here is the problem: x squared plus 5x minus 6.

2
00:00:04.630 --> 00:00:07.405
Factor a polynomial over the rational numbers.

3
00:00:08.205 --> 00:00:10.631
Write the polynomial in standard form.

4
00:00:11.082 --> 00:00:24.700
Use the AC method. Multiply a times c equals 1 times negative 6 equals negative 6. Find two numbers whose product is negative 6 and whose sum is b equals 5: 6 and negative 1.

5
00:00:25.150 --> 00:00:34.450
Factor by grouping. Group the first two and last two terms, factor each group, then factor out the common binomial. The roots are negative 6 and 1.

6
00:00:34.900 --> 00:00:36.665
Write the complete factorization.

7
00:00:37.465 --> 00:00:40.600
So the answer is (x minus 1)(x plus 6).

8
00:00:41.050 --> 00:00:47.853
x squared plus 5x minus 6 factors completely over the rationals as (x minus 1)(x plus 6).

9
00:00:48.653 --> 00:00:54.841
Expanding (x minus 1)(x plus 6) gives back x squared plus 5x minus 6.