WEBVTT

1
00:00:00.000 --> 00:00:03.471
Here is the problem: (x plus 2) to the power 4.

2
00:00:03.921 --> 00:00:07.555
Expand and simplify the polynomial into standard form.

3
00:00:08.355 --> 00:00:17.515
Distribute every product and power. Multiply each term of one factor by each term of the other; expand powers by repeated multiplication.

4
00:00:17.965 --> 00:00:20.426
Combine like terms and order by degree.

5
00:00:20.876 --> 00:00:26.565
Read off the key features. degree 4, leading coefficient 1, constant term 16.

6
00:00:27.365 --> 00:00:35.643
So the answer is x to the power 4 plus 8x cubed plus 24x squared plus 32x plus 16.

7
00:00:36.093 --> 00:00:50.164
In standard form the polynomial is x to the power 4 plus 8x cubed plus 24x squared plus 32x plus 16 (degree 4, leading coefficient 1, constant term 16).

8
00:00:50.964 --> 00:00:57.593
Spot check at x equals 2: original and expanded form both give 256.