SOLUTION: For y=f(x)x^4-10x^2+9 list all possible rational zeros of f, use synthetic division to write f in completetely factored form, list the actual zeros

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Question 732873: For y=f(x)x^4-10x^2+9
list all possible rational zeros of f, use synthetic division to write f in completetely factored form, list the actual zeros
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
The function polynomial in expanded form is x%5E4%2B0%2Ax%5E3-10x%5E2%2B0%2Ax%2B9.

Testing for -9 and +9 will fail, giving nonzero remainders.

Test for -3:
1___0___-10___0___9
___-3___9____3___-9
---------------------------------
1___-3___-1___3____0
ROOT.

Test for +3:
1___-3___-1___3
____3___0___-3
-------------------------
1___0___-1___0
ROOT.

I won't even check for -1 and +1, since I see from the corresponding quotient from the last test, x%5E2-1 is difference of two squares, %28x-1%29%28x%2B1%29. Roots are +1 and -1.

Roots found are -3, +3, -1, +1.