SOLUTION: P(x) = x4 − 2x3 − 24x2 + 50x − 25. What are all the rational zeros and the polynomial in its factored form?

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: P(x) = x4 − 2x3 − 24x2 + 50x − 25. What are all the rational zeros and the polynomial in its factored form?      Log On


   

Question 947225: P(x) = x4 − 2x3 − 24x2 + 50x − 25. What are all the rational zeros and the polynomial in its factored form?
Answer by lwsshak3(11628) About Me  (Show Source):
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P(x) = x4 − 2x3 − 24x2 + 50x − 25. What are all the rational zeros and the polynomial in its factored form?
Rational roots theorem w/synthetic division:
...0...|...1....-2.....-24.....50.....-25
...1...|...1....-1.....-25.....25......0 (1 is a zero)
...2...|...1.....1.....-23.....4....................
...3...|...1.....2....-19.....-7.................
...4...|...1.....3....-13.....-2...................
...5...|...1....4.....-5........0 (5 is a zero)
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...0...|...1....-2.....-24.....50.....-25
..-1...|...1....-3.....-21.....71.....-96........
..-2...|...1....-4.....-16.....82.....-189........
..-3...|...1....-5......-9......77.....-256.
..-4...|...1....-6.......0......50.....-225...........
..-5...|...1....-7.......9.......5........0 (-5 is a zero)
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Rational zeros: -5, 1, 5
P(x)=(x-1)(x-5)(x+5)