If (1)=0, what are all the roots of the function f(x)=x3+3x2-x-3?use the remainder theorem

Question

asked Jul 26, 2019 132k views

2 Answers

Maksim · Answer 1 · 2019-08-02T01:24:43+0000

If

, then by the remainder theorem
(f(x))/(x-1)

has a remainder of 0, which means
f(x)

is divisible by
x-1

. In fact,

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

So we know 1 is a root, and the other two roots are -1 and -3.