SOLUTION: 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. f(x)=4x^4+5x^3+9x^2+10x+2

Algebra ->  Rational-functions -> SOLUTION: 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. f(x)=4x^4+5x^3+9x^2+10x+2      Log On


   

Question 971029: 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.
f(x)=4x^4+5x^3+9x^2+10x+2
Answer by lwsshak3(11628) About Me  (Show Source):
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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.
f(x)=4x^4+5x^3+9x^2+10x+2
Use rational roots theorem with synthetic division:
...0..|......4.......5......9.....10......2.
...1..|......4.......9.....18....28.....30 (1 is upper boundary)
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...0...|......4.......5......9.....10......2.
..-1..|......4.......1......8.......2......0 (-1 is a root)
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..0......|.....4........1......8......2..
.-1/4..|.....4........0......8......0 (-1/4 is a root)
..-1....|.....4.......-3.....5.....-3..(real root exists between 0 and -1)(-1 is lower boundary)
f(x)=(x+1)(4x+1)(4x^2+8)
zeros are: -1/4, and -1