Sally is given the information ƒ(1)= 0, ƒ(-2)=0 and ƒ(3)=0. Which are the factors of the polynomial?
A)
(x-2)(x+3)(x+1)
B)
(x+2)(x-3)(x-1)
C)
(x-2)(x-3)(x-1)
D)
(x+2)(x+3)(x+1)
To find the factors of the polynomial, we can use the given information.
We know that a polynomial has a factor of (x-a) if and only if it equals zero when plugging in the value of 'a' into the polynomial.
Given that ƒ(1) = 0, this means that (x-1) is a factor of the polynomial.
Given that ƒ(-2) = 0, this means that (x+2) is a factor of the polynomial.
Given that ƒ(3) = 0, this means that (x-3) is a factor of the polynomial.
Therefore, the factors of the polynomial are (x-1)(x+2)(x-3).
Out of the options given, the correct answer is C) (x-2)(x-3)(x-1).
To determine the factors of the polynomial, we need to analyze the given information about the function ƒ(x) for different values of x.
Given that ƒ(1) = 0, we can conclude that (x-1) is a factor of the polynomial.
Similarly, given that ƒ(-2) = 0, we can conclude that (x+2) is a factor of the polynomial.
Finally, given that ƒ(3) = 0, we can conclude that (x-3) is a factor of the polynomial.
Combining these factors, the correct answer option is B) (x+2)(x-3)(x-1).
the factor theorme says that if for some f(x)
f(a) = 0 , then x-a is a factor,
take it from there
tell me what you picked and why