SOLUTION: Given the polynomial function f(x), factor f(x) into linear factors. f(x)= x^4+2x^3-19x^2-8x+60

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Given the polynomial function f(x), factor f(x) into linear factors. f(x)= x^4+2x^3-19x^2-8x+60      Log On


   

Question 1029570: Given the polynomial function f(x), factor f(x) into linear factors.
f(x)= x^4+2x^3-19x^2-8x+60
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
factor f(x) into linear factors.
f(x)= x^4+2x^3-19x^2-8x+60
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Graph::
graph%28400%2C400%2C-6%2C6%2C-10%2C10%2Cx%5E4%2B2x%5E3-19x%5E2-8x%2B60%29
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x = -2 is a zero::
Use synthetic division::
-2)....1....2....-19....-8....+60
.......1...0.....-19....30...|..0
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x = 2 is a zero::
Use synthetic division::
2)....1....0....-19....30
......1....2.....-15..|..0
Factor x^2 + 2x -15
(x+5)(x-3)
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Ans:: f(x) = (x+5)(x+2)(x-2)(x-3)
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Cheers,
Stan H.