005 Sample Final A, Question 6

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Question Factor the following polynomial completely,     

1) What does the Rational Zeros Theorem say about the possible zeros?
2) How do you check if a possible zero is actually a zero?
3) How do you find the rest of the zeros?
1) The possible divisors can be found by finding the factors of -10, in a list, and the factors of 1, in a second list. Then write down all the fractions with numerators from the first list and denominators from the second list.
2) Use synthetic division, or plug a possible zero into the function. If you get 0, you have found a zero.
3) After your reduce the polynomial with synthetic division, try and find another zero from the list you made in part a). Once you reach a degree 2 polynomial you can finish the problem with the quadratic formula.

Step 1:
First, we use the Rational Zeros Theorem to note that the possible zeros are:
Step 2:
Now we start checking which of the possible roots are actually roots. We find that 1 is a zero, and apply either synthetic division or long division to get
Step 3:
We continue checking zeros and find that -2 is a zero. Applying synthetic division or long division we can simplify the polynomial down to:
Step 4:
Now we can finish the problem by applying the quadratic formula or just finding the roots of
Final Answer:

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