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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
04/20/23 01:02 R-4 - Polynomials 2
Section R-4
P O L Y N O M I A L S
04/20/23 01:02 R-4 - Polynomials 3
• 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.
04/20/23 01:02 R-4 - Polynomials 4
•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.
04/20/23 01:02 R-4 - Polynomials 5
• 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
04/20/23 01:02 R-4 - Polynomials 6
• EXAMPLE 2Subtract (x + 2) – (x – 3) and express
answer as a single polynomial in standard form:
5
( 2) ( 3) 2 3x x x x
04/20/23 01:02 R-4 - Polynomials 7
• EXAMPLE 3Simplify x + 2 – x – 3 and express answer as
a single polynomial in standard form:
– 1
04/20/23 01:02 R-4 - Polynomials 8
• 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
04/20/23 01:02 R-4 - Polynomials 9
•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
04/20/23 01:02 R-4 - Polynomials 10
• MULTIPLYING POLYNOMIALS
FirstOuterInnerLast
Box Method
04/20/23 01:02 5.1 Multiplying Factors 11
• MULTIPLYING POLYNOMIALS
Using FOIL:• Draw Arrows• Make sure each factor is multiplied at
least once• Must be written in Standard Form
04/20/23 01:02 R-4 - Polynomials 12
• 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
04/20/23 01:02 R-4 - Polynomials 13
• 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
04/20/23 01:02 R-4 - Polynomials 14
• 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
04/20/23 01:02 R-4 - Polynomials 15
• 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!!!
04/20/23 01:02 R-4 - Polynomials 16
• 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
04/20/23 01:02 R-4 - Polynomials 17
• 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
04/20/23 01:02 R-4 - Polynomials 18
•YOUR TURNSimplify (x – 1)3 and express answer as a
single polynomial in standard form:
3 23 3 1x x x
04/20/23 01:02 R-4 - Polynomials 19
• ASSIGNMENT• Pg 42: 27-39 odd, 41-75 every 4th
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