Chapter 11 Polynomial Functions

Chapter 11 Polynomial Functions

11.1 and 11.2Finding real roots of polynomials and the Fundamental Theorem of Algebra

Sounds impressive right?!

Fundamental Theorem of Algebra

• Every polynomial with degree n has “n” number of roots (zeros, x-intercepts, solutions!)

• These can be real (rational and irrational), complex (imaginary), or a combination of both! FUN!!

graphs

X = 0, 3, -4

X = 2,

X = -5, 2i, -2i

Let’s go to the real world!

Oops! Wrong real world!

How about the real number world??

Solve each poly by factoring

Multiplicity…look we’re identical!

ID the roots and state multiplicity

𝑥3+6 𝑥2+12 𝑥+8=0

𝑥4+8 𝑥3+18 𝑥2−27=0

(x + 2)(x + 2)(x + 2)

(x + 3)(x + 3)(x + 3)(x – 1)

Rational Root Theorem

Joke Break!

• Why is the rational root problem so polite?

• It minds it’s p’s and q’s!

Find the roots

𝑥3+3 𝑥2−10 𝑥−24=0• Doesn’t factor• Use rational root theorem to ID

possible roots• Use synthetic to test for root

(remainder of zero)• Knock down to factorable poly

(usually quadratic)• Factor for the other roots• List the roots

AssignmentPg. 342 (15-22 all)