Synthetic division

[mathmarauder]

I have been asked to find all the zeros of f(x)
2x^3 + x^2 - 13x + 6
fundamental theorem of algebra tell me I have 3 zeros
2 possible positive zeros
1 possible negative zero
rational zero test (+- = plus and negative)
+-1, +-2, +-3, +-6, +-1/2, +-2/2,+-3/2,+-6/2
now the final step...synthetic division,
I know if the remainder is zero, the number we plugged in to get that
0 is the answer or one of the answers... any help please?

Ok i did the synthetic division and it seems like 2 is the only zero
find all zeroes of f(x) = 2 is this correct?

 

[Loren]

If 2 is one root, divide your original cubic by x-2. You should end up with a quadratic that easily can be solved for your other two roots.

 

[mathmarauder]

Thank you

 

[fasteddie65]

You mentioned synthetic division. Use it with 3 and get a reduced polynomial, which will be quadratic. You then have 3 options: factoring, Quadratic Formula, or completing the square.

 

[Mrspi]

You mentioned synthetic division. Use it with 3 and get a reduced polynomial, which will be quadratic. You then have 3 options: factoring, Quadratic Formula, or completing the square.

Hooray, Fast one! You're getting it now! Hints and tips are MUCH better than complete answers with no explanations....

Thank you!