Which of the following is a polynomial with roots 5, −6, and 7?
a.) f(x) = x3 − 6x2 − 30x + 37
b.) f(x) = x3 − 30x2 − 37x + 42
c.) f(x) = x3 − 6x2 − 37x + 210
d.) f(x) = x3 − 30x2 − 42x + 210

Given roots of the polynomial :  5, −6, and 7.

Therefore, zeros are x=5, x=-6 and x=7.

So, for the given zeros, factors are

(x-5)(x+6)(x-7).

Now, we need to multiply (x-5)(x+6)(x-7) those factors to get the final polynomial.

answer:

step-by-step explanation:

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.