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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
Holt McDougal Algebra Factoring Polynomials 6-4 Factoring Polynomials Holt Algebra 2 Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson.
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:
Operations on Rational Expressions Review Test Tomorrow!!!
Products and Factors of Polynomials Objective: To multiply polynomials; to divide polynomials by long division and synthetic division.
Remainder and Factor Theorems Section 7.4. The Remainder Theorem If a polynomial f(x) is divided by x-a, the remainder is the constant f(a), and Dividend=quotient.
Factoring a polynomial means expressing it as a product of other polynomials.
Exponents power base exponent. Warm-Up Find the value of each expression. 1.) 5 – ) (5 – 1) 3 3.) 4 (3 + 2) 4.) 10 ÷ 2 – 3 5.) 10 + (2 + 4) ÷ 4.
Aim: Solving Polynomials by Factoring Course: Alg. 2 & Trig. Do Now: Aim: How do we solve polynomial equations using factoring? Write the expression (x.
Notes 6.6 Fundamental Theorem of Algebra. If P(x) is a polynomial with degree n >1 with complex coefficients, then P(x) = 0 has at least one complex root.
Section 2.3 Polynomial and Synthetic Division. What you should learn How to use long division to divide polynomials by other polynomials How to use synthetic.
5.5 Apply the Remainder and Factor Theorems What you should learn: Goal1 Divide polynomials and relate the result to the remainder theorem and the factor.
6.1 Factoring Polynomials factor out a common factor.
Polynomial Factors Polynomial Factor Theorem. 7/23/2013 Polynomial Factors 2 The Remainder Theorem Polynomial f(x) divided by x – k yields a remainder.
Aim: Roots of Polynomial Equations Course: Alg. 2 & Trig. Aim: How do we find the zeros of polynomial functions? Do Now: A rectangular playing field with.
WARM UP Is x-2 a factor of x 2 - x -2. verify using synthetic division or long division.
Holt McDougal Algebra Dividing Polynomials 6-3 Dividing Polynomials Holt Algebra 2 Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson.
3.4 Rational Functions I. A rational function is a function of the form Where p and q are polynomial functions and q is not the zero polynomial. The domain.
Roots & Zeros of Polynomials How the roots, solutions, zeros, x-intercepts and factors of a polynomial function are related. 2.5 Zeros of Polynomial Functions.
Warm Up 1.Write the standard form of the quadratic function given a vertex and a point: vertex : (-4,-1) point: (-2,4) 2. State the vertex of the following.
1.8 Combinations of Functions: Composite Functions The composition of the functions f and g is “f composed by g of x equals f of g of x”
Simplify the expression Warm-up. How do you multiply fractions?
Warm-Up Factor the following expressions by pulling out things that each term has in common: 1.4x 3 + 8x xz 2.9x 2 y 3 + 3xy xy 4.
Sec Write the expression using logs: 2 x =7.2.
Holt McDougal Algebra Complex Numbers and Roots 5-5 Complex Numbers and Roots Holt Algebra 2 Warm Up Warm Up Lesson Presentation Lesson Presentation.
Lesson 3.4 – Zeros of Polynomial Functions Rational Zero Theorem Represent a polynomial equation of degree n. If a rational number, where p and q have.
1 10 pt 15 pt 20 pt 25 pt 5 pt 10 pt 15 pt 20 pt 25 pt 5 pt 10 pt 15 pt 20 pt 25 pt 5 pt 10 pt 15 pt 20 pt 25 pt 5 pt 10 pt 15 pt 20 pt 25 pt 5 pt Synthetic.
6.4 Factoring and Solving Polynomial Equations. Factor Polynomial Expressions In the previous lesson, you factored various polynomial expressions. Such.
7.1 An Introduction to Polynomials Learning Objective: To identify, classify, evaluate, add, and subtract polynomials. Also to describe the shape of the.
Chapter 5 – Quadratic Functions and Factoring 5.3 – Factoring x 2 + bx + c.
Holt McDougal Algebra Fundamental Theorem of Algebra 6-6 Fundamental Theorem of Algebra Holt Algebra 2 Warm Up Warm Up Lesson Presentation Lesson.
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