Question

If f(1) = 0, what are all the roots of the function f(x)=x^3+3x^2-x-3? Use the Remainder Theorem.
x = –1, x = 1, or x = 3
x = –3, x = –1, or x = 1
x = –3 or x = 1
x = –1 or x = 3

Answer 1

your idea?

Answer 2

Sorry I had to step away from the computer for a while, and I thought:
x = –1, x = 1, or x = 3
but it wasn't right.

Answer 3

how to attack it? don't guess, give me your strategy

Answer 4

I don't understand the Remainder Theorem at all, so I looked to see what all of the coefficients had in common. There's a negative one, a positive one, a negative three, and a positive three, so with x = –1, x = 1, or x = 3 the -1, +1, and +3 are taken care of and you can combine the -1 and the +3 to get your -3.
I know this probably makes no sense, but it's what my brain came up with in desperation.

Answer 5

if f(1) =0 that means 1 is one of the roots. So that (x-1) is one of the factor of the expression.
use long division to get other

Answer 6

do you know long division or synthetic ?

Answer 7

I have been taught both but only understand long division.

Answer 8

ok, apply it, show me your work.

Answer 9

k one minute

Answer 10

x^3+3x^2-x-3 / x-1

x^2(x-1)= x^3 -x^2

x^3+3x^2
-(x^3 -x^2)
=4x^2

4x(x-1)= 4x^2 -4x

4x^2 -x
4x^2 -4x
=3x

3(x-1)=3x -3

3x-3
-(3x -3)
=0

Answer: x^2 +4x +3

Answer 11

very very good job. so, solve for the quadratic x^2 +4x +3 , what do you have ?

Answer 12

1, 4, and 3?

Answer 13

4,3 are not the roots of that quadratic,
let solve: x^2 +4x +3 = (x+1)(x+3) ok?

Answer 14

Oh yeah! Sorry, I remember now. That makes sense. Thank you.