# Math Help - HELP! I need help finishing this problem!

1. ## HELP! I need help finishing this problem!

Here is the question as posed to me in my homework (actually... it's a take home test, so its even more important!)

f(x)= 6x^5 + 5x^4 - 35x^3 - 21x^2 + 51x + 18.

A: Find all of the zeros of f(x).

B: Write f(x) in factored form.

C: Draw an approximate sketch of f(x)

-2, -1/3, 3/2 are the three zeros that i have found using synthetic divison. The remaining equation i have left is 6x^2 - 18 which I have factored into 6(x^2 - 3). Is this the correct action to take (as in factoring it out) and what would be the remaining two zeros? Would it be -3 and 3? How do I write f(x) into factored form? And how would I draw an approximate sketch of that? IF someone could help me out... I would be forever in debt to them. THANKS IN ADVANCE!

2. Originally Posted by aweisone
-2, -1/3, 3/2 are the three zeros that i have found using synthetic divison. The remaining equation i have left is 6x^2 - 18 which I have factored into 6(x^2 - 3). Is this the correct action to take (as in factoring it out) and what would be the remaining two zeros?
yes, that is fine.

Would it be -3 and 3?
no. if you plug in x = 3 or x = -3, you do not get zero, do you?

Hint: treat this as the difference of two squares. (write $3$ as $(\sqrt{3})^2$)

How do I write f(x) into factored form?
any polynomial in x can be written in the form: $(x - a)(x - b)(x - c) ...$

where a,b,c,... are the roots of the polynomial.

And how would I draw an approximate sketch of that?
you found the zeros (i did not check if they were correct by the way, so check yourself), so mark these on the x-axis. between the zeros, check if the function is positive or negative. so for example, if one zero was 1 and another was 3, you would plug in something like 2 into the polynomial. if the value is positive, you know the graph is above the x-axis, if negative, it is below. do this for all the intervals. we have an odd degree polynomial, so one end will go to infinity while the other goes to negative infinity. when you have all the zeros marked and the positions of the graph in each intervals, just draw the curve through them....

hope that helped. i had to be somewhat vague on purpose since this is a test...