Question

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

Answer 1

Answer: D on Edg

Explanation:

Answer 2

If
`f(1)=0`, 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.