Download CCGPS Advanced Algebra

CCGPS Advanced Algebra
Name____________________________________
Unit: 2
Unit 2: Polynomial Functions
Date_____________________
Homework: 18
Standard:
Use complex numbers in polynomial identities and equations.
 MCC9‐12.N.CN.9 (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic
polynomials.
Understand the relationship between zeros and factors of polynomials.
 MCC9‐12.A.APR.2 Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the
remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).
 MCC9‐12.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.
Essential Question:
 How can you use the number of sign changes in a function to determine the number and type of real zeros
of that function?
 How can synthetic substitution be used to find the value of a function?
Key Words:
Complex Conjugate Theorem, depressed polynomial, factor of a polynomial, Factor Theorem, Fundamental
Theorem of Algebra, integer, Integral Zero Theorem, multiplicity (of a zero), polynomial function, Remainder
Theorem, repeated root, root, synthetic division, zeros
Recommended Resources:
http://www.walch.com/rr/00165
http://www.walch.com/rr/00166
http://www.walch.com/rr/00167
http://www.walch.com/rr/00168
Determine the number and type of roots for each equation using one of the given roots. Then find each root.
1. x3 – 7x + 6 = 0; 1
2. x3 – 3x2 - 25x - 21 = 0; -1
3. x3 - 4x2 – 3x + 18 = 0; 3
4. x3 + 4x2 – 3x - 18 = 0; -3
Find all the zeros of each function. Then graph each function to verify your answers.
5. f(x) = x2 + 4x – 12
6. f(x) = x3 – 3x2 + x + 5
7. f(x) = x3 – 4x2 – 7x + 10
8. f(x) x3 – 7x + 6
Write the simplest polynomial function with integral coefficients that has the given zeros.
9. -5, -1, 3, 7
10. -5, -2, 4
11. 4, 2 + 3i
12. -3, 1 - 2i