Question

f(x) = x^4 – 3x^3 – 5x^2 + 21x + 22
Use the synthetic division or long division to identify ONE zero of the function.

Answer 1

Have you come across the rational root theorem? Using this theorem, you will need fewer tries.

Answer 2

no

Answer 3

The rational root theorem says that if the function has zeroes which are rational (can be represented by fractions), then the zeroes must be of the form \(\pm \frac{p}{q}\) where p is a factor of the constant term, and q is a factor of the leading coefficient.
Invoking this theorem limits your choice of factors to \(\pm{1,2,11}\).
So you only have to do synthetic divisions by (x+1),(x-1),(x+2),(x-2),(x+11),(x-11), and you should get a zero of f(x) [ if f(x) has rational roots].
Hint: This particular f(x) has only two rational roots.

Answer 4

yeah no idea

Answer 5

If you need a review on synthetic division, best is to look at some web pages.
Synthetic division is quite tedious to show because of the formatting.
Try
http://www.purplemath.com/modules/synthdiv.htm