Download Standard Form

• WARM-UP
•
Simplify:
4
–
1.
x y
2 3
x y
2
4
(

5
x
z
)
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.
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R-4 - Polynomials
1
POLYNOMIALS
Section R-4
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R-4 - Polynomials
2
• 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
POLYNOMIALS
Refresh: Standard Form: Descending degree form in
equation.
Rewrite each polynomial in standard form.
2. 5x2 – 4 + 8x4 + x
Write terms in
descending order by
degree.
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8x4 + 5x2 + x – 4
R-4 - Polynomials
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•
EXAMPLE 1
Add (x + 2) + (x + 3) and express answer as
a single polynomial in standard form:
( x  2)  ( x  3)  x  2  x  3
2x + 5
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•
EXAMPLE 2
Subtract (x + 2) – (x – 3) and express
answer as a single polynomial in
standard form:
( x  2)  ( x  3)  x  2  x  3
5
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•
EXAMPLE 3
Simplify x + 2 – x – 3 and express answer as
a single polynomial in standard form:
–1
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•
EXAMPLE 4
Simplify (8x3 – 2x2 + 6x – 2) + (3x4 – 2x3 + x2
+ x) and express answer as a single
polynomial in standard form:
(8x3  2 x 2  6 x  2)  (3x 4  2 x3  x 2  x) 
8 x  2 x  6 x  2  3x  2 x  x  x
3
2
4
3
2
3x4 + 6x3 – x2 + 7x – 2
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•YOUR
TURN
Simplify (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
First
Outer
Inner
Last
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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5.1 Multiplying Factors
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•
EXAMPLE 1
Multiply (x + 2) (x + 3) and express answer
as a single polynomial in standard form.
( x  2)( x  3)
x 3x 2x 6
2
x  5x  6
2
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•
EXAMPLE 1
Multiply (x + 2) (x + 3) and express answer
as a single polynomial in standard form.
( x  2)( x  3)
x
+2
x
2
x
+2x
+3
+3x
+6
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R-4 - Polynomials
x  5x  6
2
13
•
EXAMPLE 2
Multiply (x – 5) (x + 5) and express answer
as a single polynomial in standard form:
( x  5)( x  5)  x  5 x  5 x  25
2
x  25
2
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•
EXAMPLE 3
Simplify (x – 4)2 and express answer as a
single polynomial in standard form:
( x  4)  ( x  4)( x  4)
2
 x  4 x  4 x  16
2
x  8 x  16
2
x  16
2
NO!!!
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•
EXAMPLE 4
Simplify (3x – 4)2 and express answer as a
single polynomial in standard form:
(3x  4)  (3x  4)(3x  4)
2
 9 x  12 x  12 x  16
2
9 x  24 x  16
2
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•
EXAMPLE 5
Simplify (x + 2)3 and express answer as a
single polynomial in standard form:
( x  2)  ( x  2)( x  2)( x  2)
2
 ( x  2 x  2 x  4)( x  2)
3
 ( x  4 x  4)( x  2)
3
2
2
 x  2 x  4 x  8x  4 x  8
2
x  6 x  12 x  8
3
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2
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•YOUR
TURN
Simplify (x – 1)3 and express answer as a
single polynomial in standard form:
x  3x  3x  1
3
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2
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•
ASSIGNMENT
• Pg 42: 27-39 odd, 41-75 every 4th
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