1. Consider the function f(x) = x4 + 4x3 – 7x2 – 22x + 24.
a.) Find the possible rational roots of f(x) = 0.
b.) Use synthetic division to divide f(x) by x – 1. Show all your work. Use your answer to explain whether or not x – 1 is a factor of f(x).
c.) Factor f(x) completely. Show all your work.
d.) Sketch the graph of f(x) by plotting the x-intercepts, finding and plotting additional points on the graph, and using what you know about the graph’s end behavior

Question

1. Consider the function f(x) = x4 + 4x3 – 7x2 – 22x + 24.
a.)	Find the possible rational roots of f(x) = 0.
b.)	Use synthetic division to divide f(x) by x – 1. Show all your work. Use your answer to explain whether or not x – 1 is a factor of f(x).
c.)	Factor f(x) completely. Show all your work.
d.)	Sketch the graph of f(x) by plotting the x-intercepts, finding and plotting additional points on the graph, and using what you know about the graph’s end behavior

zzr0ck3r · Answer

If there is a rational root then it is of the form $\dfrac{\pm1,2,3,4,6,8,12,24}{1}$

zzr0ck3r · Answer

I would google for the synthetic division part. It is going to be ugly to try and learn that on here. Much easier if you just go find an example and follow the steps.

sshayer · Answer

if x-1 is a factor,then divide by 1 (synthetic division)
you know how to do synthetic division.