How do you find the zeros of the polynomial function with equation #f(x) = x^3 +7x^2 - 4x - 28#?

1 Answer
May 4, 2016

Answer:

Using the Factor Theorem (hoping or integer factors) we find zeros at #x in {-2,+2,-7}#

Explanation:

According to the Factor Theorem if #color(blue)(1)x^3+7x^2-4x-color(red)(28)# as rational zeros
they must be factors of #color(red)(28)/color(blue)(1)#

The possible factors are therefore
#color(white)("XXX"){+-1,+-2,+-4,+-7,+-14+-28}#

Testing these factors:

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we find three zeros (as given in the "Answer" above.

Since the given expression is of degree 3 and we have 3 zeros, these 3 zeros represent all possible solutions.