Question

Find all zeros of g(x)=2x^3+x^2-22x+24 given that x=2 is a zero

Answer 1

Can I use synthetic division here?

Answer 2

factor as \((x-2)\times (\text{something})\) and then use the quadratic formula to find the zeros of the "something"
you can find it by dividing using synthetic division

Answer 3

yes, use synthetic division is easiest method
hardest method is long division
medium method is thinking about what it has to be

Answer 4

Okay. How about this..."Find all factors of x^3-x^2-5x-3 given that (x+1) is a factor"

Answer 5

Can I use synthetic division there too?

Answer 6

yes

Answer 7

So would the answer be in standard form?

Answer 8

\[x^3-x^2-5x-3 =(x+1)(whatever)\]

Answer 9

actually for this one thinking would not be too hard

Answer 10

\[x^3-x^2-5x-3 =(x+1)(x^2+bx-3)\] you only need to find the \(b\) because the first and last term are obvious

Answer 11

since \(-3x+bx=-5x\) that tells you \(b=-2\) giving
\[x^3-x^2-5x-3 =(x+1)(x^2-2x-3)\]

Answer 12

but you can use synthetic division if you find it easier

Answer 13

But it says I have to find the factors..so once I finish with the synthetic division and I have my answer in standard form, do I just factor out whatever I got from the synthetic division?

Answer 14

So I got this after doing synthetic x^2-2x-3
So would I factor that?

Answer 15

yeah that one should be easy right?

Answer 16

Yeah, sorry about my stupidity. I have a test tomorrow and I'm scrambling to learn this pellet

Answer 17

pellet? I typed in sh**