1. Write solutions of HW problems on the board.

2. HW Key: P(2) = 3; P(3) = -16; root ≈ 2.2
P(-3) = 2 and P(2) = 1
But there are 2 roots
between them.
(Answers may vary.)

3. 3.6 Polynomial Functions ~ part 1
Chapter 3
3.6 Polynomial Functions ~ part 1

4. Objectives: SWBAT: Define a polynomial
Divide polynomials using long division and synthetic division.
HW: p. 224: 82, 84, 86 (Long Division)
p. 223: (even) (Synthetic Division)

5. The following are polynomials:
The following are NOT polynomials:

6. Properties of Polynomials:
All exponents are whole numbers.
No variable is contained in a denominator.
No variable is under a radical.

7. Definition of Terms:
Constant Polynomial - consists of only a constant term.
Zero Polynomial - the constant polynomial 0.
Degree of the polynomial - the highest exponent of the variable with nonzero coefficient.
Leading coefficient – the nonzero coefficient of the highest powered variable.

8. State the degree, the leading coefficient, and the constant term of each of the polynomials:

9. Polynomial Long Division: Divide:
r. 2x – 13 – + – – + –
(3x3 + 2x2 – 8) ÷ (x2 – x + 1) = 3x + 5 r. 2x – 13
Dividend
Divisor
Quotient
Remainder

10. Students Try!!! Divide: – – + + + –
(3x4 – 3x3 – 6x2 – 6x + 12) ÷ (x3 + x2 – 2) = 3x – 6
Divisor
Quotient
Dividend

11. Synthetic Division:
Synthetic division can be used only when the divisor is x – c.
In synthetic division, you initially work with the coefficients and constants of the dividend and just the constant of the divisor.
The degree of the quotient is always 1 degree less than the dividend.

12. Use synthetic division: Divide: (2x4 – 5x3 + 3x – 8) ÷ (x – 3)

13. Students Try!!! Divide: (x5 + 5x4 + 6x3 – x2 + 4x + 29) ÷ (x + 3)

14. The Division Algorithm
(3x3 + 2x2 – 8) ÷ (x2 – x + 1) = 3x + 5 r. 2x – 3
Dividend = Divisor ● Quotient + Remainder
(3x3 + 2x2 – 8) = (x2 – x + 1) ● (3x + 5) + (2x – 3)

15. Closure:
Write 3 things that you learned today.