10/20/2015 12:04 amr-4 - polynomials1 warm-up simplify: – 1. 2. determine the area and...

04/20/23 01:02 R-4 - Polynomials 1

• WARM-UP• Simplify:

– 1. 2.

• Determine the area and circumference of a circle where the radius is 8 cm.

• Determine the length of a rectangle in which the area is 20 cm and the width is 5 cm.

4

2 3

x y

x y2 4( 5 )x z

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Section R-4

P O L Y N O M I A L S

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• REVIEW• Coefficient: The number in front of the variable.• Degree: The sum of the exponents of the variables.

ADD THE TOTAL EXPONENTS• Term: Parts of an expression that is added or

subtracted• Constant Term: The number at the end of the

equation that doesn’t have the variable.• Standard Form: Descending degree form in

equation.

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•CLASSIFYING POLYNOMIALSRefresh: Standard Form: Descending degree form in

equation.

Rewrite each polynomial in standard form.

2. 5x2 – 4 + 8x4 + x

8x4 + 5x2 + x – 4Write terms in descending order by

degree.

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• EXAMPLE 1Add (x + 2) + (x + 3) and express answer as

a single polynomial in standard form:

2x + 5

( 2) ( 3) 2 3x x x x

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• EXAMPLE 2Subtract (x + 2) – (x – 3) and express

answer as a single polynomial in standard form:

5

( 2) ( 3) 2 3x x x x

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• EXAMPLE 3Simplify x + 2 – x – 3 and express answer as

a single polynomial in standard form:

– 1

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• EXAMPLE 4Simplify (8x3 – 2x2 + 6x – 2) + (3x4 – 2x3 + x2

+ x) and express answer as a single polynomial in standard form:

3x4 + 6x3 – x2 + 7x – 2

3 2 4 3 2(8 2 6 2) (3 2 )x x x x x x x 3 2 4 3 28 2 6 2 3 2x x x x x x x

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•YOUR TURNSimplify (8x3 – 2x2 + 6x – 2) – (3x4 – 2x3 + x2

+ x) and express answer as a single polynomial in standard form:

5x4 + 10x3 – 3x2 + 5x – 2

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• MULTIPLYING POLYNOMIALS

FirstOuterInnerLast

Box Method

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• MULTIPLYING POLYNOMIALS

Using FOIL:• Draw Arrows• Make sure each factor is multiplied at

least once• Must be written in Standard Form

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• EXAMPLE 1Multiply (x + 2) (x + 3) and express answer

as a single polynomial in standard form.

( 2)( 3)x x 2x 3x 2x 62 5 6x x

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• EXAMPLE 1Multiply (x + 2) (x + 3) and express answer

as a single polynomial in standard form.

( 2)( 3)x x

x2 +2x

+3x +6

x

+3

x +2

2 5 6x x

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• EXAMPLE 2Multiply (x – 5) (x + 5) and express answer

as a single polynomial in standard form:

2 25x

2( 5)( 5) 5 5 25x x x x x

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• EXAMPLE 3Simplify (x – 4)2 and express answer as a

single polynomial in standard form:

2 16x

2 8 16x x

2( 4) ( 4)( 4)x x x 2 4 4 16x x x

NO!!!

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• EXAMPLE 4Simplify (3x – 4)2 and express answer as a

single polynomial in standard form:

29 24 16x x

2(3 4) (3 4)(3 4)x x x 29 12 12 16x x x

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• EXAMPLE 5Simplify (x + 2)3 and express answer as a

single polynomial in standard form:

3 26 12 8x x x

3( 2) ( 2)( 2)( 2)x x x x 2( 2 2 4)( 2)x x x x 2( 4 4)( 2)x x x 3 2 22 4 8 4 8x x x x x

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•YOUR TURNSimplify (x – 1)3 and express answer as a

single polynomial in standard form:

3 23 3 1x x x

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• ASSIGNMENT• Pg 42: 27-39 odd, 41-75 every 4th