1. 6-2 Polynomials and Linear Factors

2. Standard and Factored Form  Standard form means to write it as a simplified (multiplied out) polynomial starting with the highest degree term and working down to the constant term. 3x 2 + 2x – 7  Factored form means to write it as the product of two or more factors by factoring. (remember GCF first!) (x – 4)(x + 2)(x + 1)

3. Zeros  A zero is a (solution or x-intercept) to a polynomial function.  If (x – a) is a factor of a polynomial, then a is a zero (solution) of the function.  If a polynomial has a repeated solution, it has a multiple zero.  The number of repeats of a zero is called its multiplicity.

4. Finding Zeros  To find the zeros of a polynomial, we can either graph or we can factor. (2x – 1)(2x – 1)(x + 5)(x – 5)

5. Finding Zeros  To find the zeros of a polynomial, we can either graph or we can factor. (2x – 1)(2x – 1)(x + 5)(x – 5) 2x – 1=0

6. Finding Zeros  To find the zeros of a polynomial, we can either graph or we can factor. (2x – 1)(2x – 1)(x + 5)(x – 5) 2x =1

7. Finding Zeros  To find the zeros of a polynomial, we can either graph or we can factor. (2x – 1)(2x – 1)(x + 5)(x – 5) x = ½

8. Finding Zeros  To find the zeros of a polynomial, we can either graph or we can factor. (2x – 1)(2x – 1)(x + 5)(x – 5) x = ½ (multiplicity 2)

9. Finding Zeros  To find the zeros of a polynomial, we can either graph or we can factor. (2x – 1)(2x – 1)(x + 5)(x – 5) x = ½

10. Finding Zeros  To find the zeros of a polynomial, we can either graph or we can factor. (2x – 1)(2x – 1)(x + 5)(x – 5) x = ½, -5

11. Finding Zeros  To find the zeros of a polynomial, we can either graph or we can factor. (2x – 1)(2x – 1)(x + 5)(x – 5) x = ½, -5

12. Finding Zeros  To find the zeros of a polynomial, we can either graph or we can factor. (2x – 1)(2x – 1)(x + 5)(x – 5) x = ½, -5, 5

13. Remember  The following are equivalent statements:  -4 is a solution of x 2 + 3x – 4  -4 is an x-intercept of x 2 + 3x – 4  -4 is a zero of y = x 2 + 3x – 4  x + 4 is a factor of x 2 + 3x – 4