Warm Up answers 1. x 2. 3x²y 8xy² 3. 7x² - 3x 4. 1 term 5. 2 terms 6. 3 terms
Warm Up
Assignment 10/23/14 Section 6.1 Page 315: 2 12 (E) 40 58 (E) 66 Section 6.2 Page 323: 2 12 (E) 16 36 (E) 42 46 (E) 48 50 (E) (use a graphing tool such as www.desmos.com/calculator) 52, 53, 74
Objective Students will: classify polynomials by degree and term multiply binomials and find zero s of polynomials
Polynomials
Classifying Polynomials Polynomials are classified by degree number of terms P( x) 4 2 = 3x + 5x x + 2
Polynomials in standard form List the terms of the polynomials from highest to lowest P ( x) = x + 5x + 2 + 3x 2 4
Write each polynomial in standard form. Then classify it by degree and by number of terms. 9 + x 3 x 3 + 9 The term with the largest degree is x 3,so the polynomial is degree 3. It has two terms. The polynomial is a cubic binomial.
Write each polynomial in standard form. Then classify it by degree and by number of terms. b. x 3 2x 2 3x 4 3x 4 + x 3 2x 2 The term with the largest degree is 3x 4, so the polynomial is degree 4. It has three terms. The polynomial is a quartic trinomial.
Write each in standard form and classify by degree and term
Simplify (5x³ - 6x + 8) ( 3x³ - 9)
Simplify (-3x³ +2x + 8) ( 2x³ +x- 9)
Simplify (4x³ +2x 2 3) ( x³ +x 9)
5x²(6x 2) Simplify
2x²(3x 2) Simplify
-2x²(x 1) Simplify
y(y 4 )² Simplify
2w(w 2 )² Simplify
a(3a + 1 )² Simplify
Factored form 6 X 2 +4x-12 3 2 (x + 6) (x 2 ) In the factor tree each branch ends with a prime number. In the factor tree for polynomials, each branch ends with a prime linear factor.
Polynomials and Linear Factors Writing a Polynomial in Standard Form Write (x 1)(x + 3)(x + 4) as a polynomial in standard form.
Polynomials and Linear Factors Writing a Polynomial in Standard Form Write.( x 2 ) (x + 3) ( x + 4) as a polynomial in standard form.
Polynomials and Linear Factors Writing a Polynomial in Standard Form Write (x - 5) ( x + 5 ) ( x - 5 ) as a polynomial in standard form.
Polynomials and Linear Factors Writing a Polynomial in Standard Form Write ( y + 8 ) (y 1 ) ( y + 1 ) as a polynomial in standard form.
Polynomials and Linear Factors Writing a Polynomial in Standard Form Write (x + 2)(x 5)( 2x + 1) as a polynomial in standard form.
Polynomials and Linear Factors Writing a Polynomial in Factored Form Step 1: CF Write 3x 3 18x 2 + 24x in factored form. Step 2: diamond and the box
Polynomials and Linear Factors Writing a Polynomial in Factored Form Write 2x³ - 4x² +2x in factored form.
Polynomials and Linear Factors Writing a Polynomial in Factored Form Write 5x³ - 10x² - 75x in factored form.
Finding Zeros
Relative (absolute) Maximum and Relative (absolute) Minimum The maximum value is the greatest y-value of the points in a region of the graph The minimum value is the least y-value of the points in a region of the graph Relative (absolute) maximum = 8 X int. Zeros Solutions roots Relative (absolute) minimum= - 4
Find the Relative (absolute) Maximum and Relative (absolute) Minimum
Polynomials and Linear Factors Finding Zeros of a Polynomial Function Find the zeros of y = (x + 1)(x 1)(x + 3). Finding the zeros means find the x-intercepts To find the x-intercepts, let y = 0 0= (x + 1)(x 1)(x + 3). Use the zero product property
Polynomials and Linear Factors Finding Zeros of a Polynomial Function Find the zeros of y = (x 5)(x + 5 )(x 2)
Polynomials and Linear Factors Finding Zeros of a Polynomial Function Find the zeros of y = ( 2x + 1)(x - 5)(x + 10)
Polynomials and Linear Factors Write a Polynomial Function From its Zeros Write a polynomial in standard form with zeros at 2, 3, and 0.
Polynomials and Linear Factors Write a Polynomial Function From its Zeros Write a polynomial in standard form with zeros at 5,6, and-7.
Polynomials and Linear Factors Write a Polynomial Function From its Zeros Write a polynomial in standard form with zeros at -3, 3,and 4.
If a linear factor of a polynomial is repeated, then the zero is repeated. A repeated zero is called a multiple zero. linear factor (x 1 )(x + 2) (x 1 ) = 0 A multiple zero has a multiple equal to the number of times the zero occurs. In this example, the zero 1 has multiplicity of 2
Finding the Multiplicity of a Zero Find any multiple zeros of ƒ(x) = x 3 4x 2 + 4x and state the multiplicity.
Finding the Multiplicity of a Zero f(x) = (x 2)(x + 1)(x + 1) 2.