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This picture does the steps I used. The answer is in orange
Take the leading coefficient and the last coefficient, and list all their factors. In this case, the leading coefficient is 1 because it is the number in front of the highest order term. 36 is the last coefficient.
= 1: 1
= 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Next we will find all the possible rational roots. To do so, divide each of the factors by each of the factors. For each result there is a positive and negative root. In this case 1 is the only factor. Since anything divided by 1 is itself, the possible rational roots are the same as the factors of 36 (except now we have positive and negative numbers).
So the possible roots are -1, 1, -2, 2, -3, 3, -4, 4, -6, 6.... etc.
Now use synthetic division to test each of the possible roots. If the answer does not have a remainder, then it is a root. After one possible root works, use the result of the division to continue finding other roots. Let me know if you need help with this step and I will upload a picture. Otherwise, division is pretty straight forward.
After dividing the polynomial by each possible rational root, we find -2 and -3 as roots. We can express these roots as the factors (x+2) and (x+3). So after wee factor them out, we get:
(x+2)(x+3)(x^2 - 4x + 6)
Hope this helps! Rational Root Theorem is a lot of work, but it is easy once you understand it!
Next we will find all the possible rational roots. To do so, divide each of the
So the possible roots are -1, 1, -2, 2, -3, 3, -4, 4, -6, 6.... etc.
Now use synthetic division to test each of the possible roots. If the answer does not have a remainder, then it is a root. After one possible root works, use the result of the division to continue finding other roots. Let me know if you need help with this step and I will upload a picture. Otherwise, division is pretty straight forward.
After dividing the polynomial by each possible rational root, we find -2 and -3 as roots. We can express these roots as the factors (x+2) and (x+3). So after wee factor them out, we get:
(x+2)(x+3)(x^2 - 4x + 6)
Hope this helps! Rational Root Theorem is a lot of work, but it is easy once you understand it!