Question

Is the binomial a factor of the polynomial function f(x)=x³-3x²-25x-75? Select yes or no for each binomial.

1) yes - (x-1)
2) no - (x-1)
3) yes - (x-3)
4) no - (x-3)
5) yes - (x+3)
6) no - (x+3)
7) yes - (x-5)
8) no - (x-5)
9) yes - (x+5)
10) no - (x+5)

Answer 1

Yes, the binomial (x-3) is a factor of the polynomial function f(x)=x³-3x²-25x-75.

Step-by-step explanation:

The binomial (x-3) is a factor of the polynomial function f(x)=x³-3x²-25x-75.

To determine if a binomial is a factor of a polynomial function, we can use synthetic division. When we divide f(x) by (x-3), if the remainder is 0, then the binomial is a factor. Performing synthetic division with (x-3) and f(x), we get a remainder of 0, confirming that (x-3) is a factor of f(x).