## mitchelsewbaran 3 years ago What are the possible rational zeros of f(x) = 2x3 – 4x2 – 7x + 10 ? ± 1/2, ± 1, ± 2, ±5/2 , ± 5, ± 10 ± 1, ± 2, ± 5, ± 10 1/2 , 1, 2, 5/2 , 5, 10 1, 2, 5, 10

1. amistre64

this applies to the rational root thrm that takes a pool of options from the factors of the last number divided by the factors of the first

2. campbell_st

the factors of the constant are called p factors of the coefficient of the leading term are q the possible roots are p/q

3. mitchelsewbaran

i still dont understand

4. amistre64

you need to be able to determine the first and last numbers to begin with :) can you tell me what they are?

5. amistre64

also, proper form has the +- tags, so that narrows it down to the first 2 options

6. campbell_st

ok... so the factors of 10 are 1 x 10 or -1 x -10, 2 x 5 or -2 x -5 (called p) the factors of 2 are 1 x 2 or -1 x -2 (called q) so if you use p/q for the roots you will have 1/1, -1/1 1/-1 and -1/-1, then 10/1, -10/1, 10/-1 and -10/-1, 1/2, -1/2, 1/-2, -1/-2 etc... this gives all the possible rational roots