1. Finding the Zeros By Matt Selby

2. Step One Start with your equation. Let’s say, f(x)= x^3 – 6x^2 + 13x- 10 for example.

3. Step Two The next step is to use synthetic division. x^3 – 6x^2 + 13x- 10 _l 1 -6 13 -10 In order to determine what number to divide by, we type the function into a calculator and look at the graph. In this situation, the line seems to cross at the 2 mark (2,0).

4. Step 3 Next, insert the number into the synthetic division. 2 l 1 -6 13 -10 l +2 -8 10 1 -4 5 0 So we’re left with, 1x^2 -4x +5

5. Step 3 Now we take what was left, 1x^2 -4x +5 , and use quadratic formula. (x = -b + or – radical(b^2) – 4 ac) / 2a A= 1 B=-4 C= 5

6. Step 3 (cont.) X= -(-4) + or – Radical ((-4)^2 – 4(1)(5) ) / 2(1) Which becomes, 4 + or – radical (-4) /2 Which then simplifies to become, 4 + or – 2i/ 2 This simplifies to 2 + or – i

7. Step 4 So the zeros are 2 + or – i When we convert them into f(x), they go in as opposites. F(x)= ( x – 2) ( x – 2 +i)(x – 2- i)

8. Finish That’s basically all is takes to find the zeros. It’s a fairly simple concept, the trick is knowing all the other equations that are used. The end