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Use synthetic division to divide (4x 3 – 3x 2 + 2x + 1)/ (x – 1) (x 3 – x 2 – 6)/(x + 2) Warm up
Dividing a polynomial by a monomial (4y 5 – 6y y 3 – 8y 2 ) / (4y 2 )
Dividing a polynomial by a polynomial using long division (6x 2 + x – 2)/ (2x – 1)
Dividing a polynomial by a polynomial using synthetic division (2t t + 15)/ (t + 5)
Factor by grouping x 3 + x 2 – x – 1
Factor by grouping 2x 3 – 3x 2 – 2x + 3
Sum and difference of two cubes
Factor the following x y 3 – 125
Factor the following 4x 5 – 32x 2 2x x 4
Factor theorem The expression x-a is a linear factor of a polynomial if and only if the value a is a zero of the related function. --How do you find out if a is a zero of the function?
Factor theorem Is -2 a zero of the following function? Y = x 3 + x 2 – 2x
Factor theorem Is -5 a zero of the following function? Y = x 3 + 9x x -25
Factor theorem Is 3 a zero of the following function? If yes then find the other remaining zeros Y = x 3 - 9x x – 27
Write a polynomial function in standard form with the given zeros X = 5, 6, 7X = -2, 0, 1
Write a polynomial function in standard form with the given zeros X = -5, -5, 1X = 3,3,3
Solving Polynomials. Factoring Options 1.GCF Factoring (take-out a common term) 2.Sum or Difference of Cubes 3.Factor by Grouping 4.U Substitution 5.Polynomial.
Dividing Polynomials SYNTHETIC DIVISION AND LONG DIVISION METHODS.
Holt McDougal Algebra 2 Factoring Polynomials Warm Up Factor each expression. 1. 3x – 6y 2. a 2 – b 2 3. (x – 1)(x + 3) 4. (a + 1)(a 2 + 1) x 2 + 2x –
Holt Algebra Factoring Polynomials 6-4 Factoring Polynomials Holt Algebra 2 Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson.
Dividing Polynomials & The Remainder Theorem. Dividing Polynomials When dividing a polynomial by a monomial, divide each term in the polynomial by the.
5.1 – 5.6 Review Algebra 2. Exponents! Evaluate the expression: ∙ (x 3 y -5 )(x 2 y) 2 3.(3x 3 y 6 ) -2.
Warmup Divide using synthetic division using the zero given. Then factor the answer equation completely and solve for the remaining zeroes. Show.
POLYNOMIAL FUNCTIONS A POLYNOMIAL is a monomial or a sum of monomials. A POLYNOMIAL IN ONE VARIABLE is a polynomial that contains only one variable. Example:
Solving Polynomials. What does it mean to solve an equation?
Holt McDougal Algebra Factoring Polynomials Use the Factor Theorem to determine factors of a polynomial. Factor the sum and difference of two cubes.
Holt McDougal Algebra Factoring Polynomials 3-4 Factoring Polynomials Holt Algebra 2 Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson.
Warm Up Factor each expression. 1. 3x – 6y 2. a 2 – b 2 3. (x – 1)(x + 3) 4. (a + 1)(a 2 + 1) x 2 + 2x – 3 3(x – 2y) (a + b)(a – b) a 3 + a 2 + a + 1 Find.
quotient () () () ()
EXAMPLE 1 Find a common monomial factor Factor the polynomial completely. a. x 3 + 2x 2 – 15x Factor common monomial. = x(x + 5)(x – 3 ) Factor trinomial.
Unit 3 Practice Test Review. 1a) List all possible rational zeros of this polynomial: 5x 4 – 31x x 2 – 31x + 6 p 1, 2, 3, 6 q 1, 5 p 1, 2,
Section 2-2 Synthetic Division; The Remainder and Factor Theorems.
WARM UP. Homework Q’s Dividing Polynomials using Synthetic Division EQ: How is Long Division utilized to divide a polynomial functions? Assessment:
5.5 Apply the Remainder and Factor Theorem. Long Division Polynomial Long Division: process used to divide polynomials. Divide f(x) = 3x 4 – 5x + 4x –
Conjugate Pairs Theorem Every complex polynomial function of degree n 1 has exactly n complex zeros, some of which may repeat. 1) A polynomial function.
Algebra II Explorations Review ( ) Day Divide using LONG Division. Show all work. Answer:
5.3 Division of Polynomials. Dividing a Polynomial by a monomial. Divide each term of the polynomial by the monomial.
Dividing Polynomials Divide Polynomials using Long Division and Synthetic Division.
6.3 Dividing Polynomials. Warm Up Without a calculator, divide the following Solution:
a. b. To simplify this process, we can use a process called division. Synthetic division works when dividing a polynomial by. To get started, make.
Warm Up no 0, 3 x = -3. Homework Questions Section 2.2 Synthetic Division; The Remainder and Factor Theorems Objective: To use synthetic division and.
7.6 Rational Zero Theorem Objectives: 1. Identify the possible rational zeros of a polynomial function. 2. Find all the rational zeros of a polynomial.
Dividing Polynomials/Long and Synthetic Division Section 6.3.
Long and Synthetic Division. Long Division Polynomial long division can be used to divide a polynomial d(x), producing a quotient polynomial q(x) and.
6.4 F ACTORING P OLYNOMIALS Use the Factor Theorem to determine factors of a polynomial. Factor the sum and difference of two cubes. Learning Targets Why.
Products and Factors of Polynomials (part 2 of 2) Section 440 beginning on page 442.
Holt McDougal Algebra Factoring Polynomials 6-4 Factoring Polynomials Holt Algebra 2 Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson.
Rational Expressions Simplifying. Polynomial – The sum or difference of monomials. Rational expression – A fraction whose numerator and denominator are.
Lesson 2.3 Read: Pages Page 127: #1-61 (EOO)
Factor Theorem Using Long Division, Synthetic Division, & Factoring to Solve Polynomials.
5.5B – Synthetic Division. If I tell you that (x – 1) is a factor of the equation above, what does that tell you? x = 1 is a solution.
Polynomials. DegreeNameExample 0Constant 1Linear 2Quadratic 3Cubic 4Quartic 5Quintic Some of the Special Names of the Polynomials of the first few degrees:
Theorems About Roots of Polynomial Equations. Find all zeros: f(x)= x +x –x Synthetic Division one zero…need 2 more use (x – k), where.
6.5 Warm Up 1.Factor 8x Factor 5x x 2 – x – 2. 3.Factor 200x 6 – 2x 4. 4.Find the product of (2x – 3)(2x – 5). 5.Find the product of (5x.
7.3 Products and Factors of Polynomials Objectives: Multiply polynomials, and divide one polynomial by another by using long division and synthetic division.
1 Warm-up Determine if the following are polynomial functions in one variable. If yes, find the LC and degree Given the following polynomial function,
4.5 Quadratic Equations Zero of the Function- a value where f(x) = 0 and the graph of the function intersects the x-axis Zero Product Property- for all.
Using theorems to factor polynomials. If a polynomial f(x) is divided by x-k, then the remainder r = f(k) This is saying, when you divide (using synthetic.
1 Use the Remainder Theorem and the Factor Theorem. 2.3 Day 2 What You Should Learn.
5.4 – Apply the Remainder and Factor Theorems Divide 247 / / 8.
Section 7.3 Products and Factors of Polynomials.
Section 2.3 Polynomial and Synthetic Division Long Division of polynomials Ex. (6x 3 -19x 2 +16x-4) divided by (x-2) Ex. (x 3 -1) divided by (x-1) Ex (2x.
Remainder and Factor Theorem Unit 11. Definitions Roots and Zeros: The real number, r, is a zero of f(x) iff: 1.) r is a solution, or root of f(x)=0 2.)
Algebra 2. Warm Up A monomial is an expression that is either a real number, a variable or a product of real numbers and variables. A polynomial.
1 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-1 Polynomials and Polynomial Functions Chapter 5.
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