What is the range of the function y = |x |? x ≥ 0 y ≥ 0 all real numbers
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This will be a 4th degree polynomial. Our root of x = 7 in factorization form is (x-7). Our root of x = -11 in factorization form is (x+11) and the last one is a complex number. According to the conjugate root theorem, if we have 2+8i, we also HAVE to have 2-8i. In factorization form that first one is (x-(2+8i)) which simplifies to (x-2-8i). Its conjugate in factorization form is (x-2+8i). Now we will FOIL all that out. Let's start with the (x-2-8i)(x-2+8i). That multiplies out to 
. We have to combine like terms here to shorten that a bit. 
. i^2 is equal to -1, and -1(64) = -64. Now we have 
. That is 
. Now let's FOIL in another factorization. 
. That comes out to 
. One more term to go! 
. That, finally, is 
.