1. If a polynomial q(x) is divided by x – 4, the quotient is 2 𝑥 2 +3𝑥 𝑥−4 . Which of the following must be true?
q(-4) = 58
q(4) = 58
q(-4) does not exist
q(4) does not exist
Problem of the Day

2. Problem of the Day… Take 2!
Given that p(-2) = 0, p(-5) = 0, and p(4) = 0, which expression could be p(x)?
x 3 +3 x 2 −18x−40
x 3 −3 x 2 +18x−40
x 3 −3 x 2 −18x+40
x 3 −3 x 2 −18x−40
Problem of the Day… Take 2!

3. Section 5-7 Roots and Zeros

4. Then
Now
Objectives
You used complex numbers to describe solutions of quadratic equations.
Determine the number and type of roots for a polynomial equation.
Find the zeros of a polynomial function.

5. Common Core State Standards
Content Standards
N.CN.9 – Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.
A.APR.3 – Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.
Mathematical Practices
6) Attend to precision.
Common Core State Standards

6. Zeros, Factors, Roots, and Intercepts

7. Find all of the zeros of: 𝑓 𝑥 = 𝑥 3 +2 𝑥 2 +9𝑥+18
Example 3

8. Find all of the zeros of: 𝑔 𝑥 = 𝑥 4 +50 𝑥 2 +49
Example 3

9. Find all of the zeros of: ℎ 𝑥 = 𝑥 4 −3 𝑥 3 − 𝑥 2 −27𝑥−90
Example 3

10. Find all of the zeros of: 𝑓 𝑥 = 𝑥 4 −3 𝑥 3 −9 𝑥 2 +77𝑥+150
Example 3

11. Complex Conjugates Theorem

12. Write a polynomial function of least degree with integral coefficients, the zeros of which include -5, 4i.
Example 4

13. Write a polynomial function of least degree with integral coefficients, the zeros of which include 6, -2i.
Example 4

14. Write a polynomial function of least degree with integral coefficients, the zeros of which include -1, 4, 3i.
Example 4

15. p.363 #11, 15, 35, 38, 41, 42, 50 – 52, 61
Homework

16. Which of the following functions has only real zeros? a) b) c) d)
Problem of the Day