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Understanding Polynomials and Factoring: A Comprehensive Guide

Explore essential concepts of polynomials and factoring, including adding, subtracting, and multiplying polynomials, special products, solving polynomial equations, and factoring techniques. Understand the parts of an expression, terms, coefficients, exponents, and constants. Enhance your knowledge of monomials, binomials, trinomials, degrees, and types of polynomials with practical examples. Practice adding and subtracting polynomials and simplify expressions in algebra. Master polynomial operations for improved math skills.

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Understanding Polynomials and Factoring: A Comprehensive Guide

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  1. Do Now 2/22/10 • Copy HW in your planner. • Text p. 557, #4-28 multiples of 4, #32-35 all • In your notebook on a new page define the parts of the expression below. Use the following words: terms, coefficients, constants, exponents -3x² + 2x + 8

  2. Chapter 9 “Polynomials and Factoring” • (9.1) Add and subtract polynomials • (9.2) Multiply polynomials • (9.3) Find special products of polynomials • (9.4) Solve polynomial equations in factored form • (9.5) Factor x² + bx + c • (9.6) Factor ax² + bx + c • (9.7) Factor special products • (9.8) Factor polynomials completely

  3. Parts of an Expression Remember this??? Coefficient the number part of the term (negative sign included) -3x² + 2x + 8 Terms of the expression Constant Term that has no variable

  4. Objective • SWBAT add and subtract polynomials

  5. Section 9.1 “Add and Subtract Polynomials” Monomial a number, a variable, or the product of a number and one or more variables with whole number exponents -3x Degree = 1 7 Degree = 0 Degree of a Monomial the sum of the exponents of the variables in the monomial Degree = 6 x³yz²

  6. Polynomial a monomial, or the sum (or difference) of monomials Degree = 1 Degree = 0 Degree = 3 –3x +7 – x³ Write a polynomial with exponents decreasing from left to right. Degree of a Polynomial the greatest degree of its terms -1 Leading Coefficientthe coefficient of the first term when exponents are decreasing from left to right.

  7. Types of Polynomials Trinomial Binomial polynomial with 3 terms polynomial with 2 terms 2x³+ x – 7 4 – 3x

  8. To Be or Not To Be a Polynomial… 14 – 3x Yes; 1st degree binomial 4x³ Yes; 3rd degree monomial -3 2y No; negative exponent 9 + 3x² + 2yz³ Yes; 4th degree trinomial n 6x + 2x No; variable exponent

  9. Add Polynomials Like Terms terms that have the same variable (2x³ – 5x² + x) + (2x² + x³ – 1) You can add polynomials using the vertical or horizontal format. Vertical Format Horizontal Format (2x³+ x³) + (2x²– 5x²)+ x– 1 2x³ – 5x² + x x³ + 2x² – 1 3x³ – 3x² + x – 1 3x³ – 3x² + x – 1

  10. Subtract Polynomials Like Terms terms that have the same variable (4n² + 5) – (-2n² + 2n – 4) You can subtract polynomials using the vertical or horizontal format. Vertical Format Horizontal Format 4n² + 5 (4n²+ 2n²)– 2n + (5+ 4) – (-2n² +2n – 4) +(2n² -2n + 4) 6n² – 2n + 9 6n² – 2n + 9

  11. Adding and Subtracting Polynomials

  12. Simplifying Polynomials in Geometry • What is the perimeter of the trapezoid? Perimeter is the distance around a figure. Add together each of the sides. 3x – 2 3x - 2 + 2x + 2x + 1 + 5x - 2 (reorder terms) 2x 2x + 1 3x + 2x + 2x + 5x – 2 – 2 + 1 (combine like terms) 12x – 3 5x – 2

  13. Homework Text p. 557, #4-28 multiples of 4, #32-35 all

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