Question

given -4 is a root, find the remaining real roots for f(x)=x^3 + 2x^2 - 11x - 12

Answer 1

that means
\[x^3+2x^2-11x-12=(x+4)(something)\]
the "something" will be a quadratic so you can find the roots of it

Answer 2

you can find the something by
long division ( a pain)
synthetic division (very snappy)
or just thinking about what it has to be

Answer 3

to basically do (x+4)(something that when multiplied will equal the equation)?

Answer 4

right

Answer 5

do you know how to do synthetic division?

Answer 6

I don't remember much of it...

Answer 7

well then lets just think
synthetic division is real real easy but almost impossible two write here

Answer 8

isnt it where you write down all the coefficients and then multiply the numbers by the root?

Answer 9

\[x^3 + 2x^2 - 11x - 12=(x+4)(ax^2+bx+c)\] it should be pretty clear that it will be
\[x^3+2x^2-11x+12=(x+4)(x^2+bx-3)\] right? we just don't know \(b\) yet

Answer 10

yes it is
multiply and add etc

Answer 11

but if you got how i wrote the second line above, we can find \(b\) real easy

Answer 12

when i did synthetic division, i got what seems to be a remainder of 40...

Answer 13

Im not sure exactly how to do it the other waay...

Answer 14

then you screwed up because the remainder has to be zero
lets find \(b\)
did you understand how i got \[x^3+2x^2-11x+12=(x+4)(x^2+bx-3)\]

Answer 15

sorry for the bad writing but this is what i did..