how do i solve this equation x^4-x^3-x^2-x-2=0 also how do i fine the number and type of root?

Question

compassionate · Answer

You can solve by adding like terms then factoring it.

anonymous · Answer

first guess some obvious numbers 
try $f(1)$ and if that doesn't work try $f(-1)$

compassionate · Answer

Hmm... @satellite73 , this is a polynomial.

anonymous · Answer

what grade levle is this????!!!!

anonymous · Answer

$$f(x)=x^4-x^3-x^2-x-2$$
$$f(1)=1-1-1-1-2\neq 0$$

anonymous · Answer

yes, i know it is a polynomial
do you have any idea how to find the zeros of a polynomial of degree 4?

anonymous · Answer

im a sophomore and its algebra 2

compassionate · Answer

Of course I do.

anonymous · Answer

really? love to hear it
ok now we know that 1 is not a zero, try $-1$

anonymous · Answer

how would i factor it?

anonymous · Answer

don't try to factor it until you find the zeros

anonymous · Answer

$$f(x)=x^4-x^3-x^2-x-2$$
$$f(-1)=1+1-1+1-2=0$$ got it on the second try!

anonymous · Answer

now you can factor, since you know $-1$ is a zero, it must factor as 
$$x^4-x^3-x^2-x-2=(x+1)(something)$$

compassionate · Answer

When I did Algebra II, my professor taught us to factor by grouping first. 

Huh. That's odd.

anonymous · Answer

find the "something" by division
synthetic division is easiest

anonymous · Answer

we are being taught both synthetic division and factoring. but i don't understand how to group and factor this problem!

anonymous · Answer

factor by grouping might work if the polynomial has four terms and has been cooked up nicely 
@madison.hall00  don't try it
divide 
forget factoring

compassionate · Answer

Yeah. Listen to Satellite. I think the next step is synthetic division and the zero remainders are your roots. 

Carry on!

anonymous · Answer

haha thank you guys!