Question

Which of the following is a root of the polynomial shown below?
f(x)=x^3-4x^2-11x+30
A. -3
B. 0
C. 1
D. 6

Answer 1

\[f(x) = x^3-4x^2-11x+30\]

so given that polynomial, we need to use the rational root test.
So using the last term (that's 30)
find all factors of 30
plug in x = one of the factors of 30 and see if your result is 0
If it's 0, then we have a root
If it's not 0 we don't have root
and if all roots don't work, then the rational root test fails

Answer 2

is it C?

Answer 3

oh... we have multiple choice... that's good. We can use either -3,1, or 6.
Hint: 0 doesn't work.

Is it C?
let's try it
let x = 1
\[f(1) = 1^3-4(1)^2-11(1)+30\]
try computing f(1)

Answer 4

I got 1-16-11+30 = 0 unless I did something wrong

Answer 5

something isn't right for the 4(1)^2 part

Answer 6

(1)^2 means write 1 twice
(1)(1)
so for that part
4(1)(1)
what's 4 x 1 x 1 ?

Answer 7

oh oops is it 1-4-11+30=16 so it's not c?

Answer 8

not c. so cross that out

Answer 9

so it's either -3 or 6

Answer 10

Oh I got it. I think it's a? -27-36+33-30=-0

Answer 11

oops 0*

Answer 12

\[f(-3) = (-3)^3-4(-3)^2-11(-3)+30\]
\[f(-3) = -27-4(9)+33+30\]
\[f(-3) = -27-36+33+30\]
\[f(-3) = -63+63\]
\[f(-3) = 0\]
so yes -3 is a root of the polynomial
you can just write 0. a negative sign isn't required.

Answer 13

okay thanks!! I get it now :)

Answer 14

yay :D