1. 3.7 Day 2 When all roots are potentially imaginary or irrational

2. This is the only time you will be given a head start. Where do imaginary or irrational roots come from? So, if you are given one imaginary/irrational root, you know another. The conjugate.

3. Now, there are 2 ways to solve 1.You could synthetically divide in the first root, then its conjugate. You must get remainder of 0 both times, and with the second imaginary/irrational root, there should be nice coefficients. Then you will continue as usual.

4. OR If you can find the polynomial that the roots came from, you can divide the larger polynomial in (it must be done with long division, though) and then break down the quotient. Lets apply this theory to the prime factorization of 10406

5. How do you find where the roots came from? A little friend called The Sum and Product Rule PolynomialR1R1 R2R2 SumProduct

6. How do you find where the roots came from? A little friend called The Sum and Product Rule

7. Lets practice a problem both ways