2. Heinz has a list of possible functions. Pick one of the g(x) functions below, show how to find the zeros, and then describe to Heinz the other key features of g(x).
o g(x) = x3 – x2 – 4x + 4
o g(x) = x3 + 2x2 – 9x – 18
o g(x) = x3 – 3x2 – 4x + 12
o g(x) = x3 + 2x2 – 25x – 50
o g(x) = 2x3 + 14x2 – 2x – 14

Question

2.	Heinz has a list of possible functions. Pick one of the g(x) functions below, show how to find the zeros, and then describe to Heinz the other key features of g(x). 
o	g(x) = x3 – x2 – 4x + 4
o	g(x) = x3 + 2x2 – 9x – 18
o	g(x) = x3 – 3x2 – 4x + 12
o	g(x) = x3 + 2x2 – 25x – 50
o	g(x) = 2x3 + 14x2 – 2x – 14

reemii · Answer

did you already meet a technique to find zeros of a third degree polynomial?

anonymous · Answer

I am clueless about this. @reemii

reemii · Answer

if you had the time to draw many points of the graph, you might find (approximately) several roots (or all 3) of the functions.

otherwise:
take the first one: g(x) = x^3-x^2-4x+4.

the usual technique is to try out several x's and see if one of them is a zero.
so we try x=0, x=1, x=-1, x=2, x=-2 etc.
do you see that g(1) =  0 ?

reemii · Answer

after finding one zero, we can use euclidian division or hornet's method to factorize g(x)..
does it ring a bell?

reemii · Answer

Horner*