Question 947223
P(x) = x5 − x4 − 5x3 + x2 + 8x + 4. Find all real zeros.
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Rational Roots Theorem with synthetic division
...0...|....1......-1......-5......1......8.......4
...1...|....1.......0......-5.....-4......4.......8
...2...|....1.......1......-3.....-5......-2......0 (2 is a root or zero)
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...0...|....1.......1......-3.....-5......-2
...2...|....1.......3.......3......1........0 (2 is a root of mult.2)
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...2...|....1.......3.......3......1
..-1...|....1......2........1.....0  (-1 is a root or zero)
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{{{P(x)=(x-2)^2(x+1)(x^2+2x+1)}}}
{{{P(x)=(x-2)^2(x+1)(x+1)^2}}}
{{{P(x)=(x-2)^2(x+1)^3}}}
zeros are:-1(mult.3), 2(mult.2)