Answer:
-4, 1, and 5
Step-by-step explanation:
To find the zeros of a polynomial, I like to get rid of the x's and keep the coefficients like this: x³ - 2x² - 19x + 20 -> 1 -2 -19 20
Now, we do some long division, let's try it out
For every number on the third row, multiply by it by the 1 and carry it over
1 | 1 -2 -19 20
0
1
Multiply the first coefficient by 1 and add it to the second coefficient
1 | 1 -2 -19 20
0 1
1 -1
Multiply the second coefficient by 1 and add it to the third coefficient
1 | 1 -2 -19 20
0 1 -1
1 -1 -20
I think you get the idea
1 | 1 -2 -19 20
0 1 -1 -20
1 -1 -20 0
We end up with a remainder of 0, meaning 1 is one of the zeros
Usually, you would just plug and test, but I'll save you some time and spoil the fun for you; the remaining zeros are -4 and 5
-4 | 1 -1 -20
0 -4 20
1 -5 0
5 | 1 -5
0 5
0 0
