Question

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.

Answer 1

which part are you having trouble with ?

Answer 2

the first part

Answer 3

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

Answer 4

okay, then let me ask you some questions

do you know what a "rational" number is ?

Answer 5

not really.

Answer 6

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

Answer 7

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

Answer 8

i understand.

Answer 9

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

Answer 10

x^2-2x+1

Answer 11

what you did was probably

\[(x-1)^2 = x^2 -2x +1\]

Answer 12

the step you took is called "expanding"
the opposite step is called "factoring"

so for example \[x^2 +5x +6 = (x+2)(x+3)\]

Answer 13

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

Answer 14

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

Answer 15

okay, I just want to demonstrate the difference between a), b), and c), so bare with me.

could you factor \[x^2-1\]

Answer 16

(x-1)(x+1)

Answer 17

i appreciate the help btw

Answer 18

fantastic

now find the solution of

\[x^2+2x+5 =0\]

Answer 19

i have to use the quadratic formula dont i?

Answer 20

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

Answer 21

Are you still here ?