+292 1.)
Factor the polynominal function over the complex numbers
f(x)=x^4-x^3-2x-4
2.)
Enter the number of complex zeros for the polynomial function in the box.
f(x)=x^5+4x^3-5x
3.)
What are the zeros od the polynomial function?
f(x)=x^4+2x^3-16x^2-2x+15
Select each correct answer.
-5
-1
0
1
3
5
Thank you (:
+6251 \(x^4 -x^3 - 2x - 4 = (x^4-4)-(x^3+2x) = \\ (x^2-2)(x^2+2) - x(x^2+2) = \\ (x^2+2)(x^2-x-2)=\\ (x+\sqrt{2}i)(x-\sqrt{2}i)(x-2)(x+1)\)
2) A fifth degree polynomial will have 5 complex zeros
3) \(x^4+2x^3-16x^2-2x+15 = \\ (x^4-16x^2+15) +(2x^3-2x) =\\ (x^2-15)(x^2-1)+2x(x^2-1) = \\ (x^2+2x-15)(x^2-1) = \\ (x-3)(x+5)(x-1)(x+1) \\ \\ \text{and the zeros can be read off as }\\ \\ x=3,~-5,~1,~-1\)
