Question 583198: Question: Use the Rational Zeros Theorem to find all the real zeros of the polynomial function  . Use the zeros to factor f over the real numbers.
I know the possible factors of the constant are 1, 2, 4, 8, -1, -2, -4, -8. But using the remainder theorem, none of them are actually possible factors (none of those factors have a remainder of 0). But when I graph it on a graphing calculator, there are zeros (x-intercepts). So I'm a little confused here. Thank you.
Found 2 solutions by scott8148, lwsshak3:
Answer by scott8148(6628)   (Show Source):
Answer by lwsshak3(11628)  (Show Source):
You can put this solution on YOUR website! Question: Use the Rational Zeros Theorem to find all the real zeros of the polynomial function
f(x) = x^4 - x^3-6x^2+4x+8. Use the zeros to factor f over the real numbers.
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Rational Roots Theorem:
Using synthetic division:
...0....|.....1....-1.......-6.......4.....8
...1....|.....1.....0.......-6.....-2....-8
...2....|.....1.....1........-4....-4......0 (2 is a zero)
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..,,0...|.....1..... 1......-4......-4
..-1...|.....1......0.......-5......4
..-2...|.....1.....-1.......-2.....0 (-2 is a zero)
f(x)=(x-2)(x+2)(x^2-x-2)
f(x)=(x-2)(x+2)(x-2)(x+1)
Zeros: -2, -1, & 2 (multiplicity 2)
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