Question

Please help!!

Answer 1

Use the Rational Zeros Theorem to write a list of all possible rational zeros of the function.

f(x) = 3x^3 + 39x^2 + 39x + 27

Answer 2

So I think the idea is to factor the coefficient of the leading term and the constant term, and then the possible rational zeros are found by dividing all the factors of the constant term by factors of the leading term.

So in this case, factors of 3 are 1 and 3; factors of 27 are 1, 3, 9, 27. So possible rational zeros are plus or minus(for all of the following) 1/1=1, 1/3, 1/9, 1/27, 3/1=3. 3/3=1, 3/9=1/3, and 3/27=1/9. So +/-1, +/-1/3, +/-1/9, +/-1/27, +/-3.

Now to find the actual roots, you would plug in possible zeros for x until you get one for which the expression does equal zero, to get one root for when the polynomial equals zero. Then do synthetic/long division to obtain a quadratic polynomial which we can factor or use the quadratic formula to solve.

Answer 3

OH! I did all that but I used 39 rather than 27! So the constant is the number without the x then?

Answer 4

how do i find the roots if it's plus or minus?

Answer 5

yeah, that's the constant term. not sure i understand the other question. are you trying to factor the equation? if +/-1 are possible rational zeros, then +1 and -1 are both possible rational zeros, so try plugging each of them in to see if either one works out to zero. You only need to find one.

Answer 6

oh okay! Thanks so much!! I really appreciate the help!

Answer 7

np

Answer 8

fyi i screwed up the terms above, should be all the factors of 27 divided by the factors of 3 and looks like I put the factors fo 3 divided by 27. It's factors of the constant over factors of the leading coefficient. Sorry, need sleep...

Also, don't think this one actually factors with rational roots, if you're looking for that.