SOLUTION: Find all zeros of the function and write the polynomial as a product of linear factors. {{{ f(x) = x^3 + 8x^2 + 22x + 20 }}} A. {{{ f(x)=(x+2)(x+3+i)(x+3-i) }}} B. {

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find all zeros of the function and write the polynomial as a product of linear factors. {{{ f(x) = x^3 + 8x^2 + 22x + 20 }}} A. {{{ f(x)=(x+2)(x+3+i)(x+3-i) }}} B. {      Log On


   

Question 471807: Find all zeros of the function and write the polynomial as a product of linear factors.
++f%28x%29+=+x%5E3+%2B+8x%5E2+%2B+22x+%2B+20++

A. ++f%28x%29=%28x%2B2%29%28x%2B3%2Bi%29%28x%2B3-i%29++
B. ++f%28x%29=%28x%2B2%29%28x%2B3%2Bi%29%28x-3-i%29++
C. ++f%28x%29=%28x-1%29%28x%2B3%2Bi%28sqrt3%29%29%28x%2B3-i%28sqrt3%29%29++
D. ++f%28x%29=%28x%2B1%29%28x%2B3%2Bi%28sqrt3%29%29%28x-2-i%28sqrt3%29%29++
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) = x^3 + 8x^2 + 22x + 20
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I graphed "f" and found a Real root at x = -2
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Then, using synthetic division I get:
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-2)....1...8....22....20
........1...6....10...|..0
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Solve x^2+6x+10 = 0
x = [-6 +- sqrt(36-4*10)]/2
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x = [-6 +- sqrt(-4)]/2
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x = -3 +- i
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Answer: A
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cheers,
Stan H.
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A. ++f%28x%29=%28x%2B2%29%28x%2B3%2Bi%29%28x%2B3-i%29++
B. ++f%28x%29=%28x%2B2%29%28x%2B3%2Bi%29%28x-3-i%29++
C. ++f%28x%29=%28x-1%29%28x%2B3%2Bi%28sqrt3%29%29%28x%2B3-i%28sqrt3%29%29++
D. ++f%28x%29=%28x%2B1%29%28x%2B3%2Bi%28sqrt3%29%29%28x-2-i%28sqrt3%29%29++