+0

# math help

+1
34
1
+216

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

-5

-1

0

1

3

5

Thank you (:

Johnnyboy  Oct 24, 2018
#1
+2714
+1

$$x^4 -x^3 - 2x - 4 = (x^4-4)-(x^3+2x) = \\ (x^2-2)(x^2+2) - x(x^2+2) = \\ (x^2+2)(x^2-x-2)=\\ (x+\sqrt{2}i)(x-\sqrt{2}i)(x-2)(x+1)$$

2) A fifth degree polynomial will have 5 complex zeros

3) $$x^4+2x^3-16x^2-2x+15 = \\ (x^4-16x^2+15) +(2x^3-2x) =\\ (x^2-15)(x^2-1)+2x(x^2-1) = \\ (x^2+2x-15)(x^2-1) = \\ (x-3)(x+5)(x-1)(x+1) \\ \\ \text{and the zeros can be read off as }\\ \\ x=3,~-5,~1,~-1$$

Rom  Oct 24, 2018