SOLUTION: Math 150 Find all of the real zeros and write the polynomial as a product of linear factors. Show all work. x,cubed - 11x,squared

SOLUTION: Math 150 Find all of the real zeros and write the polynomial as a product of linear factors. Show all work. x,cubed - 11x,squared - 15x + 325

Question 527608: Math 150 Find all of the real zeros and write the polynomial as a product of linear factors. Show all work.
x,cubed - 11x,squared - 15x + 325

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Math 150 Find all of the real zeros and write the polynomial as a product of linear factors. Show all work.
x,cubed - 11x,squared - 15x + 325
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x^3 - 11x^2 - 15x + 325
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I graphed and found a zero at x = -5
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Use synthetic division to find the other zeros:
-5)....1....-11....-15...325
........1.....-16....65..|..0
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Quotient: x^2-16x+65
x = [16 +- sqrt(16^2-4*65)]/2
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x = [16 +- sqrt(-4)]/2
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x = 8+(1/2)2i or x = 8-(1/2)2i
Note: These are not Real Number zeroes
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f(x) = (x+5)(x^2-16x+65)
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Cheers,
Stan H.
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