# Finding zeros after using synthetic division.

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• Apr 6th 2008, 09:43 PM
theevilp0ptart
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?
• Apr 6th 2008, 09:47 PM
mathceleb
Quote:

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.
• Apr 6th 2008, 10:15 PM
theevilp0ptart
Quote:

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!
• Apr 6th 2008, 10:30 PM
Mathstud28
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