WEBVTT

1
00:00:00.000 --> 00:00:04.389
Here is the problem: x squared plus 11x plus 24.

2
00:00:04.839 --> 00:00:07.544
Factor a polynomial over the rational numbers.

3
00:00:08.344 --> 00:00:10.654
Write the polynomial in standard form.

4
00:00:11.104 --> 00:00:24.223
Use the AC method. Multiply a times c equals 1 times 24 equals 24. Find two numbers whose product is 24 and whose sum is b equals 11: 8 and 3.

5
00:00:24.673 --> 00:00:34.576
Factor by grouping. Group the first two and last two terms, factor each group, then factor out the common binomial. The roots are negative 8 and negative 3.

6
00:00:35.026 --> 00:00:36.884
Write the complete factorization.

7
00:00:37.684 --> 00:00:40.958
So the answer is (x plus 3)(x plus 8).

8
00:00:41.408 --> 00:00:49.094
x squared plus 11x plus 24 factors completely over the rationals as (x plus 3)(x plus 8).

9
00:00:49.894 --> 00:00:56.953
Expanding (x plus 3)(x plus 8) gives back x squared plus 11x plus 24.