mgb5e_ppt_5_3

# mgb5e_ppt_5_3 - x 4(3 x 4(3 x 4 2 =(3 x 4(3 x 4 =(3 x(3 x 4...

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§ 5.3 Multiplying Polynomials

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Martin-Gay, Beginning Algebra, 5ed 2 Multiplying polynomials If all of the polynomials are monomials, use the associative and commutative properties. If any of the polynomials are not monomials, use the distributive property before the associative and commutative properties. Then combine like terms. Multiplying Polynomials
Martin-Gay, Beginning Algebra, 5ed 3 Multiply the following. (3 x 2 )( 2 x ) = (3)( 2)( x 2 · x ) = 6 x 3 (4 x 2 )(3 x 2 – 2 x + 5) = (4 x 2 )(3 x 2 ) – (4 x 2 )(2 x ) + (4 x 2 )(5) Distribute. = 12 x 4 – 8 x 3 + 20 x 2 Multiply the monomials. Multiplying Polynomials Example: (3 x 2 )(– 2 x )

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Martin-Gay, Beginning Algebra, 5ed 4 Multiply. (2 x – 4)(7 x + 5) = 2 x (7 x + 5) – 4(7 x + 5) = 14 x 2 + 10 x – 28 x – 20 = 14 x 2 – 18 x – 20 Multiplying Polynomials Example:
Martin-Gay, Beginning Algebra, 5ed 5 Multiply (3 x + 4) 2 Remember that a 2 = a · a , so (3 x + 4) 2 = (3

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Unformatted text preview: x + 4)(3 x + 4). (3 x + 4) 2 = (3 x + 4)(3 x + 4) = (3 x )(3 x + 4) + 4(3 x + 4) = 9 x 2 + 12 x + 12 x + 16 = 9 x 2 + 24 x + 16 Multiplying Polynomials Example: Martin-Gay, Beginning Algebra, 5ed 6 Multiply (5 x – 2 z ) 2 (5 x – 2 z ) 2 = (5 x – 2 z )(5 x – 2 z ) = (5 x )(5 x – 2 z ) – 2 z (5 x – 2 z ) = 25 x 2 – 10 xz – 10 xz + 4 z 2 = 25 x 2 – 20 xz + 4 z 2 Multiplying Polynomials Example: Martin-Gay, Beginning Algebra, 5ed 7 Multiply (2 x 2 + x – 1)( x 2 + 3 x + 4) (2 x 2 + x – 1)( x 2 + 3 x + 4) = (2 x 2 )( x 2 + 3 x + 4) + x ( x 2 + 3 x + 4) – 1( x 2 + 3 x + 4) = 2 x 4 + 6 x 3 + 8 x 2 + x 3 + 3 x 2 + 4 x – x 2 – 3 x – 4 = 2 x 4 + 7 x 3 + 10 x 2 + x – 4 Multiplying Polynomials Example:...
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mgb5e_ppt_5_3 - x 4(3 x 4(3 x 4 2 =(3 x 4(3 x 4 =(3 x(3 x 4...

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