AM3.2b To Use Synthetic Division To Find All Roots, Part 1

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Presentation transcript:

10-11-17 AM3.2b To Use Synthetic Division To Find All Roots, Part 1 The current temperature is zero degrees! Pop, when they say the temperature is zero… Does that mean there is no temperature at all? Got ID?

Active Learning Assignment?

Opener: Find the next numbers in the sequence: (Don’t say it out loud, just wait) 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ___, ___, ___, … 89 144 233 These is called the Fibonacci Sequence. Each number is the sum of the two previous numbers. These numbers happen in Nature a great deal.

Given P(x) = x2 + 7x + 12, then to factor: PRE-LESSON: Terminology: Given P(x) = x2 + 7x + 12, then to factor: 0 = x2 + 7x + 12 ® 0 = (x + 4)(x + 3) FACTORS Solving: x = -4 or x = -3 ROOTS OR ZEROS OR SOLUTIONS x axis (y = 0) x = -4 x = -3

* THE FUNDAMENTAL THEOREM OF ALGEBRA: Given P(x) can be factored. If P(x) is a polynomial of degree n and n > 0 , then the equation P(x) = 0 has exactly n roots. These roots are complex (real and/or imaginary) numbers and not necessarily unique*. This means that if you have a: 2nd degree polynomial, then there are 2 roots. 3rd degree polynomial, then there are 3 roots. 4th degree polynomial, then there are 4 roots. Etc. *For example, x2 – 6x + 9 = 0 factors to (x – 3) (x – 3) = 0 and the root is “3”, with a multiplicity of 2. Or, you can list 3 twice.

LESSON: Given a polynomial equation and one of its roots, use Synthetic Division to find the remaining roots: Same as (x – 2) 2 2 5 -23 10 4 18 -10 2 9 -5 (a) (b) (c) Now, we need to finish factoring by sight or by the quadratic formula.

We can factor this by sight or by the quadratic formula. Thus, the zeros or roots of the polynomial are:

Active Learning Assignment: {Ans} P 61: # 19 {-1, ½, 3} , 20 {-2, -½, 2/3 }