9.2 - Multiplying Polynomials

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Presentation transcript:

9.2 - Multiplying Polynomials Do NOW Is this expression a polynomial? If so, write it in standard form and determine its highest degree, type, leading coefficient, and constant term. x3 + 4x2 + 8 x3 + x4y2 + x–2 Find the sum or difference 3) (3x2 – 2x + 9) + (x2 + 2x – 4) 4) (–4x2 + 3x – 1) – (x2 + 2x – 6) 7/5/2019 2:26 AM 9.2 - Multiplying Polynomials

9.2 - Multiplying Polynomials Worksheet Key 7/5/2019 2:26 AM 9.2 - Multiplying Polynomials

Multiplying of Polynomials Section 9.2 7/5/2019 2:26 AM 9.2 - Multiplying Polynomials

Multiplying Monomials Any term that is considered ONE term If the variable has two bases, think, BASE, BASE, ADD. [add the bases] If the variables have power upon power, think, POWER, POWER, MULTIPLY [multiply the powers] 7/5/2019 2:26 AM 9.2 - Multiplying Polynomials

9.2 - Multiplying Polynomials Example 1 Multiply (5x3) (4x5) 7/5/2019 2:26 AM 9.2 - Multiplying Polynomials

9.2 - Multiplying Polynomials Example 2 Multiply (5x2y3)3 7/5/2019 2:26 AM 9.2 - Multiplying Polynomials

9.2 - Multiplying Polynomials Example 3 Multiply (–2x3y)4 7/5/2019 2:26 AM 9.2 - Multiplying Polynomials

9.2 - Multiplying Polynomials Your Turn Multiply (–3a4bc2)3 7/5/2019 2:26 AM 9.2 - Multiplying Polynomials

9.2 - Multiplying Polynomials Example 4 Multiply 5x(2x3 + 6) 7/5/2019 2:26 AM 9.2 - Multiplying Polynomials

9.2 - Multiplying Polynomials Example 5 Multiply –3x2(5x2 + 6x – 1) 7/5/2019 2:26 AM 9.2 - Multiplying Polynomials

9.2 - Multiplying Polynomials Your Turn Multiply –5x3(2x2 – 9x + 2) 7/5/2019 2:26 AM 9.2 - Multiplying Polynomials

Multiplying Binomials FOIL Method: FIRST: Multiply the first term in the first bracket and first term in the second bracket OUTER: Multiply the first term in the first bracket and second term in the second bracket INNER: Multiply the second term in the first bracket and first term in the second bracket LAST: Multiply the second term in the first bracket and second term in the second bracket Simplify the expression by combining like terms Check using your graphing calculator by looking at the graph and at y1 = y2 7/5/2019 2:26 AM 9.2 - Multiplying Polynomials

Multiplying Binomials Box Method: Create a 2x2 box with each factor going on top and on the side Multiply the first term in the top and first term in the left side for box #1 Multiply the second term in the top and first term in the left side for box #2 Multiply the first term in the top and second term in the left side for box #3 Multiply the second term in the top and second term in the left side for box #4 Simplify the expression by combining like terms 7/5/2019 2:26 AM 9.2 - Multiplying Polynomials

9.2 - Multiplying Polynomials Assignment 7/5/2019 2:26 AM 9.2 - Multiplying Polynomials

9.2 - Multiplying Polynomials Example 6 Multiply (x + 2)(x + 3) 7/5/2019 2:26 AM 9.2 - Multiplying Polynomials

9.2 - Multiplying Polynomials Example 6 (using Box) Multiply (x + 2)(x + 3) 7/5/2019 2:26 AM 9.2 - Multiplying Polynomials

Example 6 Calculator Check Multiply (x + 2)(x + 3) 7/5/2019 2:26 AM 9.2 - Multiplying Polynomials

9.2 - Multiplying Polynomials Example 7 Multiply (x + 3)(x – 5) 7/5/2019 2:26 AM 9.2 - Multiplying Polynomials

9.2 - Multiplying Polynomials Your Turn Multiply (x – 3)(x – 5) 7/5/2019 2:26 AM 9.2 - Multiplying Polynomials

9.2 - Multiplying Polynomials Example 8 Multiply (x – 5)(3x + 4) 7/5/2019 2:26 AM 9.2 - Multiplying Polynomials

9.2 - Multiplying Polynomials Example 9 Multiply (x – 4)(3x + 2) 7/5/2019 2:26 AM 9.2 - Multiplying Polynomials

9.2 - Multiplying Polynomials Your Turn Multiply (4x – 1)(x + 5) 7/5/2019 2:26 AM 9.2 - Multiplying Polynomials

9.2 - Multiplying Polynomials Example 10 Multiply (2x – 1)(5x + 3) 7/5/2019 2:26 AM 9.2 - Multiplying Polynomials

9.2 - Multiplying Polynomials Example 11 Multiply (3x – 1)(4x + 9) 7/5/2019 2:26 AM 9.2 - Multiplying Polynomials

9.2 - Multiplying Polynomials Your Turn Multiply (8x + 11)(6x – 1) 7/5/2019 2:26 AM 9.2 - Multiplying Polynomials

9.2 - Multiplying Polynomials Review Add (x – 3) + (–x2 + 2x + 4) 7/5/2019 2:26 AM 9.2 - Multiplying Polynomials

9.2 - Multiplying Polynomials Example 12 Multiply (x – 3)(–x2 + 2x + 4) 7/5/2019 2:26 AM 9.2 - Multiplying Polynomials

9.2 - Multiplying Polynomials Example 13 Multiply (x + 2)(3x2 – 4x + 1) 7/5/2019 2:26 AM 9.2 - Multiplying Polynomials

9.2 - Multiplying Polynomials Your Turn Multiply (2x2 – 3x – 4)(x + 7) 7/5/2019 2:26 AM 9.2 - Multiplying Polynomials

9.2 - Multiplying Polynomials Example 14 Find the perimeter and area of a rectangle which length is x – 5 and width is 3x + 1. 7/5/2019 2:26 AM 9.2 - Multiplying Polynomials

9.2 - Multiplying Polynomials Example 15 Find the perimeter and area of a triangle which sides are x + 5 and height is x + 6. 7/5/2019 2:26 AM 9.2 - Multiplying Polynomials

9.2 - Multiplying Polynomials Your Turn Find the perimeter and area of a rectangle which length is x + 5 and width is 3x + 1. 7/5/2019 2:26 AM 9.2 - Multiplying Polynomials

9.2 - Multiplying Polynomials Assignment Worksheet 7/5/2019 2:26 AM 9.2 - Multiplying Polynomials