Part 1: Find the polynomial f(x) that has the roots of –2, 5 of multiplicity 2. (4 points)

Part 2: Explain how you would verify the zeros of f(x). (4 points)
I forgot how to do this help pls

Question

Part 1: Find the polynomial f(x) that has the roots of –2, 5 of multiplicity 2. (4 points) 

Part 2: Explain how you would verify the zeros of f(x). (4 points)
I forgot how to do this help pls

campbell_st · Answer

well 1 solution is 

f(x) = (x + 2)(x - 5)^2

to prove

distribute to get the polynomial and then use the factor theorem by finding 

f(-2) and f(5) if both give an answer of zero they are factors.

anonymous · Answer

oh then set them equal to 0 right ? okay thanks

campbell_st · Answer

no... when you have 

f(x) = x^3 +....... 

substitute x = -2 or f(-2) and show it is equal to zero.... 

this is known as the factor theorem... 

(x + a) is a factor of a polynomial if f(-a) = 0

anonymous · Answer

ohhhh okay its coming back to me, thanks so much :)