x^4+x^3+8X^2+9x-9
write the polynomial as (a) the product of factors that are irreducible over the rationals, (b) as the product of linear and quadratic factors that are irreducible over the reals, and (c) in completely factored form.

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- yuki

which part are you having trouble with ?

- iNeedHelpPlease

the first part

- iNeedHelpPlease

if i can get that then rest of the problem should be easy

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## More answers

- yuki

okay, then let me ask you some questions
do you know what a "rational" number is ?

- iNeedHelpPlease

not really.

- yuki

it is a long story if we went through the details, but the shortest way to say it is "fractions"

- yuki

so 0.1 is rational since it is 1/10
0.7878787878... is rational since it is 78/99
-10 is rational since it is -10/1

- iNeedHelpPlease

i understand.

- yuki

knowing this, I want you to factor \[x^2 -1\]

- iNeedHelpPlease

x^2-2x+1

- yuki

what you did was probably
\[(x-1)^2 = x^2 -2x +1\]

- yuki

the step you took is called "expanding"
the opposite step is called "factoring"
so for example \[x^2 +5x +6 = (x+2)(x+3)\]

- iNeedHelpPlease

my mistake. i know how to factor and expand and what not. im just having trouble factoring that equation

- iNeedHelpPlease

if i can get that factored then i believe i will be able to solve the rest of the equation.

- yuki

okay, I just want to demonstrate the difference between a), b), and c), so bare with me.
could you factor \[x^2-1\]

- iNeedHelpPlease

(x-1)(x+1)

- iNeedHelpPlease

i appreciate the help btw

- yuki

fantastic
now find the solution of
\[x^2+2x+5 =0\]

- iNeedHelpPlease

i have to use the quadratic formula dont i?

- yuki

yes, that's my point could you use it ?

- yuki

Are you still here ?

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