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Warm Ups

Warm Ups. Simplify the following… 2(4 + x) x(x – 3x 2 + 2) 5x – 2 + 6x 2x 2 + 5x – 11x 2 + 1 8x(4x 2 ). Chapter 8.1 and 8.2. Adding, Subtracting and Multiplying Polynomials. Vocabulary. Polynomial – A monomial or sum of monomials.

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Warm Ups

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  1. Warm Ups • Simplify the following… • 2(4 + x) • x(x – 3x2 + 2) • 5x – 2 + 6x • 2x2 + 5x – 11x2 + 1 • 8x(4x2)

  2. Chapter 8.1 and 8.2 Adding, Subtracting and Multiplying Polynomials

  3. Vocabulary • Polynomial – A monomial or sum of monomials. • Monomial – A number, variable, or product of a number and 1 or more variables. • 5x • Binomial – The sum of two monomials. • 2x2 + 7 • Trinomial – The sum of three monomials. • x3 – 10x + 4

  4. Degrees of polynomials • Degree of a Polynomial – The greatest degreeof any term in the polynomial. • Degree 0 = Constant • Degree 1 = Linear • Degree 2 = Quadratic • Degree 3 = Cubic • Example: 5x3 + 6x2 – 2 Degree is 3 (Cubic)

  5. Complete the Chart…

  6. Standard Form of a Polynomial • Write the terms in order from greatest to least degree. • 4x3 – 5x2 + 2x – 7 • Your Turn… Write these in standard form. • 3x2 + 4x5 – 8x • x + 5x3 – 2x2– 7x6+ 10

  7. Add the Polynomials • Method 1: Combine Like Terms!!! • (2x2 + 5x – 7) + (3 – 4x2 + 6x) • Method 2: Align and Combine!!! • (3x + x3 – 5) + (4x2 – 4x + 2x3 + 8)

  8. Subtract the Polynomials • Method: Distribute the negative. Then, solve by adding. • (3 – 2x + 2x2) – (4x – 5 + 3x2) • (7x + 4x3 – 8) – (3x2 + 2 – 9x)

  9. Multiplying a Polynomial by a Monomial (Start of 8.2) • -3x2(7x2 – x + 4)

  10. Simplify the Expression • 2x(-4x2 + 5x) – 5(2x2 + 20)

  11. Solve Equations with Polynomials on both Sides • 2x(5x – 2) + 3x(2x + 6) + 8 = x(4x + 1) + 2x(6x – 4) + 50 • x(x + 3) – x(x – 4) = 9x – 16

  12. Homework 8.1 8.2

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