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.
which part are you having trouble with ?
the first part
if i can get that then rest of the problem should be easy
okay, then let me ask you some questions do you know what a "rational" number is ?
not really.
it is a long story if we went through the details, but the shortest way to say it is "fractions"
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
i understand.
knowing this, I want you to factor \[x^2 -1\]
x^2-2x+1
what you did was probably \[(x-1)^2 = x^2 -2x +1\]
the step you took is called "expanding" the opposite step is called "factoring" so for example \[x^2 +5x +6 = (x+2)(x+3)\]
my mistake. i know how to factor and expand and what not. im just having trouble factoring that equation
if i can get that factored then i believe i will be able to solve the rest of the equation.
okay, I just want to demonstrate the difference between a), b), and c), so bare with me. could you factor \[x^2-1\]
(x-1)(x+1)
i appreciate the help btw
fantastic now find the solution of \[x^2+2x+5 =0\]
i have to use the quadratic formula dont i?
yes, that's my point could you use it ?
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