A polynomial function f(x) with real coefficients has the given degree, zeros, and solution point.

Question

Degree: 3

Zeros: -3, 3 + √3i

Solution point: f(-1) = -172

(a) Write the function in completely factored form.

f(x) =

(b) Write the function in polynomial form.



f(x) =

Answer 1

Unfortunately this is a lot of pencil pushing. You are given 2 solutions one of which is a complex number. Since complex solutions always occur in pairs of conjugates the third solution is 3-3i. I am assuming you mean the first complex solution is 3+3i

To write in factored form we have a(x+3)[x-(3+3i)](x+[3+3i)]

y= a(x+3)(x-3-3i)(x-3+3i) when you multiply out the last 2 terms you get (x^2-6x+18)

so y = a(x+3)(x^2-6x+18) Use the point (-1,172) to solve for a

172 = a( 2)( 1+6+18)

a= 172/50= 86/25

So equation in factored for is y= (86/25)(x+3)(x^2-6x+18)

I will leave it to you to foil the last 2 factors to put this in standard polynomial form