Use the rational zeros theorem to write a list of all potential rational zeros.

f(x) = x3 - 10x2 + 9x - 24

  {±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24}

Step-by-step explanation:

Since the leading coefficient is 1, any rational zeros will be divisors of -24.

Comment on rational zeros

If the leading coefficient is not one, then rational zeros will be the ratio of a divisor of 24 to a divisor of the leading coefficient.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for