# Thread: Finding zeros after using synthetic division.

1. ## Finding zeros after using synthetic division.

Use synthetic division to divide g(x)=x^3-17x^2+90x-144 by x-8. Use the result to find all zeros of g.

I got x^2-9x+12 for the quotient with -48 remainder.

Is this correct?
The problem is, how am I supposed to find all zeros when the divisor I am expected to use has a remainder? By the way the question is worded, do you think I am supposed to find a divisor that works?

2. Originally Posted by theevilp0ptart
Use synthetic division to divide g(x)=x^3-17x^2+90x-144 by x-8. Use the result to find all zeros of g.

I got x^2-9x+12 for the quotient with -48 remainder.

Is this correct?
The problem is, how am I supposed to find all zeros when the divisor I am expected to use has a remainder? By the way the question is worded, do you think I am supposed to find a divisor that works?
theevil,

The roots for your cubic are 3, 6, and 8. I got that from here:

Soving Cubic Equations

Your discriminant was less than 0, which means the cubic has 3 real unique roots.

Since you want to divide by x - 8, you can use the synthetic division calculator I posted in the computer software forum also located here:

Synthetic Division

Dividing your cubic by (x - 8), I get $x^2 - 9x + 18$

That's a quadratic equation that you can easily solve for your last 2 roots.

Check out the math for the synthetic division to see where you went astray. Based on how close you and I are, I bet it was your last step in the constant column for synthetic division.

Let me know if you have questions.

3. Originally Posted by mathceleb
theevil,

The roots for your cubic are 3, 6, and 8. I got that from here:

Soving Cubic Equations

Your discriminant was less than 0, which means the cubic has 3 real unique roots.

Since you want to divide by x - 8, you can use the synthetic division calculator I posted in the computer software forum also located here:

Synthetic Division

Dividing your cubic by (x - 8), I get $x^2 - 9x + 18$

That's a quadratic equation that you can easily solve for your last 2 roots.

Check out the math for the synthetic division to see where you went astray. Based on how close you and I are, I bet it was your last step in the constant column for synthetic division.

Let me know if you have questions.
Oh... I see I made I simple math mistake in my addition. That changed the whole problem. Thank you for the help!

4. ## Just to let you know

if you get a remainder when synthetically dividing it means that your divisor is not a proper divisor(not sure if these terms work for polynomials) of your polynomial