WEBVTT

1
00:00:00.000 --> 00:00:05.271
Here is the problem: (2x plus 3)(x squared minus 4x plus 5).

2
00:00:05.721 --> 00:00:09.367
Expand and simplify the polynomial into standard form.

3
00:00:10.167 --> 00:00:19.525
Distribute every product and power. Multiply each term of one factor by each term of the other; expand powers by repeated multiplication.

4
00:00:19.975 --> 00:00:22.448
Combine like terms and order by degree.

5
00:00:22.898 --> 00:00:28.552
Read off the key features. degree 3, leading coefficient 2, constant term 15.

6
00:00:29.352 --> 00:00:34.994
So the answer is 2x cubed minus 5x squared minus 2x plus 15.

7
00:00:35.444 --> 00:00:46.450
In standard form the polynomial is 2x cubed minus 5x squared minus 2x plus 15 (degree 3, leading coefficient 2, constant term 15).

8
00:00:47.250 --> 00:00:52.660
Spot check at x equals 2: original and expanded form both give 7.