Chapter 4 Review Polynomials.

Slides:

Advertisements

Similar presentations

5.5 and 5.6 Multiply Polynomials

Advertisements

Warm - up x2 – 24x 4x(x – 6) 2. 2x2 + 11x – 21 (2x – 3)(x + 7)

4.3 Solve x2 + bx +c = 0 by Factoring

Chapter 6 Section 4: Factoring and Solving Polynomials Equations

Bell Problem Perform the indicated operation. (x -5)(x2 – 5x + 7)

10.7 Factoring Special Products

5.3 – Polynomials and Polynomial Functions Definitions Coefficient: the numerical factor of each term. Constant: the term without a variable. Term: a number.

Add, Subtract, Multiply Polynomials

6 – 4: Factoring and Solving Polynomial Equations (Day 1)

Day 1 – Polynomials Multiplying Mrs. Parziale

10.1 Adding and Subtracting Polynomials

Products and Factors of Polynomials

Section 5.4 Factoring FACTORING Greatest Common Factor,

Intermediate Algebra A review of concepts and computational skills Chapters 4-5.

Section 5.1 Polynomials Addition And Subtraction.

Factoring Polynomials

Factoring Polynomials. 1.Check for GCF 2.Find the GCF of all terms 3.Divide each term by GCF 4.The GCF out front 5.Remainder in parentheses Greatest Common.

10/16/2015Math KM1 Chapter 6: Introduction to Polynomials and Polynomial Functions 6.1 Introduction to Factoring 6.2 FactoringTrinomials: x 2 +bx+c.

6.4 Factoring Polynomial Equations * OBJ: Factor sum & difference of cubes Do Now: Factor 1) 25x 2 – 492) x 2 + 8x + 16 (5x + 7)(5x – 7) (x + 4)(x + 4)

1 linearf (x) = mx + bone f (x) = ax 2 + bx + c, a  0quadratictwo cubicthreef (x) = ax 3 + bx 2 + cx + d, a  0 Degree Function Equation Common polynomial.

Adding and Subtracting Polynomials Section 0.3. Polynomial A polynomial in x is an algebraic expression of the form: The degree of the polynomial is n.

Factoring and Solving Polynomial Equations Chapter 6.4.

Multiplying Polynomials. Multiply monomial by polynomial.

2.4 Factor and Solve Polynomial Equations p. 111 Name two special factoring patterns for cubes. Name three ways to factor a polynomial. What is the difference.

Objective: 6.4 Factoring and Solving Polynomial Equations 1 5 Minute Check  Simplify the expression

Sullivan Algebra and Trigonometry: Section R.4 Polynomials Objectives of this Section Recognize Monomials Recognize Polynomials Add, Subtract, and Multiply.

Chapter 9.1 Notes: Add and Subtract Polynomials Goal: You will add and subtract polynomials.

13.01 Polynomials and Their Degree. A polynomial is the sum or difference of monomials. x + 3 Examples: Remember, a monomial is a number, a variable,

Objective - To recognize and factor a perfect square trinomial. Find the area of the square in terms of x. Perfect Square Trinomial.

Factoring Review Jeopardy.

Objectives: Students will be able to…  Write a polynomial in factored form  Apply special factoring patterns 5.2: PART 1- FACTORING.

Warm-Up Exercises Multiply the polynomial. 1.(x + 2)(x + 3) ANSWER x 2 + 5x + 6 ANSWER 4x 2 – 1 2.(2x – 1)(2x + 1) 3. (x – 7) 2 ANSWER x 2 – 14x + 49.

WARM UP SOLVE USING THE QUADRATIC EQUATION, WHAT IS THE EXACT ANSWER. DON’T ROUND.

Chapter 11 Polynomials 11-1 Add & Subtract Polynomials.

Warm - up Factor: 1. 4x 2 – 24x4x(x – 6) 2. 2x x – 21 (2x – 3)(x + 7) 3. 4x 2 – 36x + 81 (2x – 9) 2 Solve: 4. x x + 25 = 0x = x 2 +

Section 6.3 Special Factoring. Overview In this section we discuss factoring of special polynomials. Special polynomials have a certain number of terms.

Factor and Solve Polynomial Equations 2.3 (GREEN book)

Factoring Polynomials. 1.Check for GCF 2.Find the GCF of all terms 3.Divide each term by GCF 4.The GCF out front 5.Remainder in parentheses Greatest Common.

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.

Identifying Terms, Factors, and Coefficients (3.1.1) February 1st, 2016.

Factor and Solve Polynomial Equations Homework Questions?

Polynomial – a monomial or sum of monomials Can now have + or – but still no division by a variable. MonomialBinomialTrinomial 13x 13x – 4 6x 2 – 5x +

Warm-Up Exercises EXAMPLE 1 Find a common monomial factor Factor the polynomial completely. a. x 3 + 2x 2 – 15x Factor common monomial. = x(x + 5)(x –

5.3 Notes – Add, Subtract, & Multiply Polynomials.

Adding and Subtracting Polynomials

Polynomials and Polynomial Functions

Polynomials & Factoring

Section 6.4: Factoring Polynomials

Polynomial Equations and Factoring

Factoring Polynomials

Do Now: Factor the polynomial.

Factoring Polynomials

Add, Subtract, Multiply Polynomials

Warm - up x2 – 24x 4x(x – 6) 2. 2x2 + 11x – 21 (2x – 3)(x + 7)

Factoring Quadratics.

Identifying Terms, Factors, and Coefficients (3.1.1)

Polynomials and Polynomial Functions

Lesson 9.1 How do you add and subtract polynomials?

Polynomials and Polynomial Functions

5.4 Factor and Solve Polynomial Equations

Factor Special Products

Polynomials and Polynomial Functions

4.1 Introduction to Polynomials

Section 9.7 “Factor Special Products”

Add, Subtract, Multiply Polynomials

3.4 Solve by Factoring (Part 1)

Factoring Polynomials First: Look for a GCF 4 Second: Number of Terms 2 3 Cubes Squares Perfect Square Trinomial Grouping X 2 – 9 X 3 – 27 = (x - 3)

Do Now 3/4/19 Take out your HW from last night.

Factoring Polynomials, Special Cases

Presentation transcript:

Chapter 4 Review Polynomials

Degree of a Monomial Degree of a Polynomial Coefficient 4x2y3z3 Degree = Coefficient = 4x2y2z2 + 3xy3z + 7x4y3z3 Degree of the polynomial =

Laws of Exponents When multiplying variables, add the exponents When raising a monomial to a power, multiply the exponents 3x2(4xy3)(y2)= 12x3y5 (2x2y3)4 = 16x8y12

Multiplying Polynomials (3x + 1)2 (3x + 2) (5x + 7) (3x + 2) (5x2 + 7x - 1) (3x + 1)3

Factoring GCF Grouping Perfect Square Trinomials with a=1 Difference of Squares Sum and Difference of Cubes

Special Products- Review You need to be able to quickly recognize special products trinomials Perfect Square Trinomials a2 + 2ab + b2 = (a + b)2 a2 - 2ab + b2 = (a - b)2 Difference of Squares a2 – b2 = (a +b)(a – b) Sum and Difference of Cubes a3 + b3 = (a + b) (a2 - ab + b2) a3 - b3 = (a - b) (a2 + ab + b2)

Factoring- What pattern do you see? x2 + 2x + 1 Perfect square trinomial (x + 1)2 16x2 – 9 Difference of squares (4x-3)(4x+3) 9x2- 12x + 4 (3x – 2)2 8x3 – 27 Difference of cubes (2x – 3)(4x2 + 6x + 9)

Solving Polynomial Equations Get everything = 0 Factor Set each factor = 0 and solve for the variable x2= x + 30 x2- x – 30 = 0 (x + 5)(x – 6)= 0 {-5, 6}

Word problems A rectangle is twice as long as it is wide. If its length is increased by 4cm and its width is decreased by 3cm, the new rectangle formed has an area of 100 cm2. Find the length and width of the original rectangle. Width = 8cm, Length = 16 cm

Frame/deck

Baseball Problem

Volume of a Box Problem