Thread: Use the given zero to find the remaining zeros of each polynomial function

1. Use the given zero to find the remaining zeros of each polynomial function

Finding the zero's of P(x) 3x^3-29x^+92x+34. The given zeros are 5+3i

2. Originally Posted by renebran
Finding the zero's of P(x) 3x^3-29x^+92x+34. The given zeros are 5+3i
If $5 + 3i$ is a zero, then so is $5 - 3i$.

So $x - (5 + 3i)$ and $x - (5 - 3i)$ are factors.

Therefore so is $[x - (5 + 3i)][x - (5 - 3i)]$

$= x^2 - x(5 - 3i) - x(5 + 3i) + (5 + 3i)(5 - 3i)$

$= x^2 - 5x + 3ix - 5x - 3ix + 25 + 9$

$= x^2 - 10x + 34$.

So divide your polynomial by $x^2 - 10x + 34$ in order to find the third factor (and third zero).

3. Originally Posted by Prove It
If $5 + 3i$ is a zero, then so is $5 - 3i$.

So $x - (5 + 3i)$ and $x - (5 - 3i)$ are factors.

Therefore so is $[x - (5 + 3i)][x - (5 - 3i)]$

$= x^2 - x(5 - 3i) - x(5 + 3i) + (5 + 3i)(5 - 3i)$

$= x^2 - 5x + 3ix - 5x - 3ix + 25 + 9$

$= x^2 - 10x + 34$.

So divide your polynomial by $x^2 - 10x + 34$ in order to find the third factor (and third zero).
This is where I'm having the problem. I'm not sure how to divide the polynomial .

4. Originally Posted by renebran
This is where I'm having the problem. I'm not sure how to divide the polynomial .
Use long division.