Question

f(x) = x^4 – 3x^3 – 5x^2 + 21x + 22
Use the Rational Roots Theorem to identify all possible roots of the function f(x).
+-1,2,11,22 i just have this and don't get the rest

Use the synthetic division or long division to identify ONE zero of the function.

State the remaining polynomial. Then find another zero.

Find all remaining zeros of the function.

Answer 1

You've identified all the factors of 22, and the roots of 1 are =1 and -1.
Look at the numbers you get when you divide the roots of 22 by 1 or by -1.

If I put the into the polynomial, do I get zero for any of them?

Answer 2

no

Answer 3

Check that more carefully. 1/1 = 1 f(1)=1-3-5+21+22= 36
2/1 = 2 f(2)=16-24-20+42+22= ?

1/(-1)=-1 f(-1)=?

Answer 4

you have no idea how lost i am

Answer 5

Probably not. But let's see if we can figure out where you are. Do you know what the root of a polynomial is?

Answer 6

not really no

Answer 7

f(-1)=1+3-5-21+22=0

Answer 8

OK. So the root of a polynomial is a number I can plug in for x that
gives f(x)=0. So, for f(x)= 3*x-6, x=2 is a root because 3*2-6=0.

Answer 9

So we are looking for numbers that we can put in for x that will give us f(x)=0.

Answer 10

-1, and for the second one -2

Answer 11

Now we're making progress. So, if I know that -1 is a root, then its
always true that f(x)= (x-(-1))*g(x), where g(x) is a smaller polynomial in x.
So, by synthetic division, I can find g(x). Remember synthetic division?

Answer 12

nope lol

Answer 13

im just gonna turn this in and hope for the best thank you

Answer 14

Ok. You might try out a few more guesses for the roots(there are only four)
by trying different combinations of the two sets of factors. Good Luck.