Lesson #7- Polynomials

A POLYNOMIAL is the sum or difference of many unlike MONOMIALS.

ex. 1 5a + 7b ex. 2 12x2 + 5x - 2

Math Gods write the terms with the highest first and go in descending order.

ex. 3 12x7 + 6x4 – 7x2 + 7

eg. 1 Adding Polynomials: Group like terms

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3x 2 + 5x +10x

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8xy 2 + 9x 2y + 5xy 2

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6a+ 7a+12b+ 5b

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7y + 6 + 8y 2 +10

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3x 2 +15x

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13xy 2 + 9x 2y

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13a+17b

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8y 2 + 7y +16

eg. 2 Subtracting Polynomials

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7x − (5x +10x)

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8x 2 + 4x − (6x 2 + 2x)

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4a+ 7b− (12a− 5b)

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7c + 6c 2 − (8c 2 −10)

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−8x

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2x 2 + 2x

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−8a+12b

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−2c 2 + 7c +10

eg. 3 Multiplying Polynomials

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3x(5x 2 + 2x)

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−5(2x +1)

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−2x 2 3x + 5( )

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2

3x 2 6x 3 − 9x + 3( )

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15x 3 + 6x 2

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−10x − 5

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−6x 3 −10x 2

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4x 5 − 6x 3 + 2x 2

Flash to the Polynomial

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1) Simpliy : 3x 2 +10x 2 − 6x + 4x

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2) Simplify : 3a+ 5b− (7a+ 9b)

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3) True or False. A monomial can

have a negative exponent.

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4) True or False. LIKE TERMS

are monomials with the same

var iables raised to the same

powers.

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5) Circle the monomials

5a 7a5b7 y−10 6 12x 4

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6) True or False : A polynomial has

at least two UNLIKE TERMS.

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7) Simplify 3x + 7y − (2x − 6y)

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8) Is 4x 3 − 7x +10 a trinomial?

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Solutions

1) 13x2 - 2x2) -4a - 4b3) False4) True5) 7a5b7, 6 & 12x4

6) True7) x +13y8) Yes

Homework

pg. 57 Activity #1pg. 57-58 #1a-d,2ac,3-5pg. 59 #6aceg