Question

how do I write this polynomial function in standard form? the fraction is throwing me off.

given zeros are, x= -2,0,1/3,1

Answer 1

I've never actually worked backwards doing polynomial functions but,

if x = -2 then it should've been (x + 2), same with the rest, (x - 1/3) and (x - 1)

x(x+2)(x-1/3)(x-1)

(x^2 + 2x)(x - 1/3)(x-1)

(x^3 -1/3x^2 + 2x^2 -2/3x)(x - 1)

\(\ \sf \Large (x^3 -\dfrac{1}{3}x^2 + 2x^2 -\dfrac{2}{3}x)\)\(\ \sf \Large ( x - 1) \)

\(\ \sf \Large (x^3 -\dfrac{5x^2}{3} -\dfrac{2}{3}x)(x-1)\)

\(\ \sf \Large (x^4 -x^3 -\dfrac{5x^3}{3} + \dfrac{5x^2}{3} -\dfrac{2}{3}x^2 + \dfrac{2}{3}x)\)

So if my calculations are correct I think this is what you meant, \(\ \sf \Large f(x) = (x^4 -x^3 -\dfrac{5x^3}{3} + \dfrac{5x^2}{3} -\dfrac{2}{3}x^2 + \dfrac{2}{3}x) \)

I did the calculation on wolfram I didn't feel like adding the fractions >.<

Answer 2

I think I made a small mistake on one of them, when I tried graphing them it gave me http://prntscr.com/37v51z

Answer 3

I'm not actually typing. >.>

Answer 4

thank you for taking the time!

Answer 5

What's it actually asking you, does it have options? Curious if my calculation was correct :>