SOLUTION: Find all real and complex zeros of the polynomial, and write p(x) as the product of linear factors. P(x)=x^4-9x^2+4x+12

Question 1050510: Find all real and complex zeros of the polynomial, and write p(x) as the product of linear factors.
P(x)=x^4-9x^2+4x+12
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
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Find all real and complex zeros of the polynomial, and write p(x) as the product of linear factors.
P(x)=x^4-9x^2+4x+12
~~~~~~~~~~~~~~~~~~~~~~~~

Apply grouping to factor P(x):

 =  =  =  =  = . 

So, one root is x = -3.

Next, transform and factor the polynomial Q(x) = x^3 - 3x^2 + 4.
Add and distract x^2 and then apply grouping, again:

 =  =  =  =  = .

The roots of the polynomial Q(x) are -1, -2, 2.

Answer. The roots of the polynomial P(x) are -3, -2, -1, and 2.

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