Algebra II –Wilsen
Unit 4: Higher Order Polynomials
Day Four
BLOCKS 1 and 3
Review
Factor and graph the x and y-intercepts of the following:
(a)
f (x) = x ( 5x – 2 ) ( x 2 + 1)
(c)
f (x) = ( 3x – 5 ) ( x 2 + 5 ) ( x 2 – 5 ) ( x 3 – 8 )
(b)
f (x) = x ( x 2 – 7 ) ( x 3 + 1)
Factoring: Sum and Difference of Cubes
Example 1
Get the following into intercept form, and give x and y intercepts.
(a)
y = x 3 + 64
(b)
y = w 3 – 27
(c)
y = 16b 5 + 686b 2
(d)
y = 16z 5 – 250z 2
(e)
y = 8x 4 + 8x 3 – 27x – 27
Techniques for Factoring… So Far
ALWAYS TAKE OUT ANY GCF FIRST!
If 2 terms:
If 3 terms:
Difference of squares
Sum of cubes
Difference of cubes
Quadratic form (
)(
)
If 4 or more even numbers of terms:
Grouping
Factor each of the following. Again, remember our goal here is to be able to find all real xintercepts.
1)
y = 27x 3 – 125
2)
y = x 5 + 2x 4 – 9x 3 – 18x 2
3)
y = x 6 – 26x 3 – 27
4)
f (x) = x 3 – 3x 2 – x + 3
5)
f (x) = x 4 – 9x 2
6)
f (x) = x 5 + x 4 – 3x 3 – 3x 2 – 4x – 4
Unit 4 Homework 4 (4.4)
Factor the following sums and differences of cubes completely.
1.
x3 + 8
2.
8a 3 + 1
3.
x3 − y3
4.
64 x 3 y 3 − 1
5.
a 6 + b3
6.
(abc) 3 − 125
7.
x 30 − y12
8.
b 3 − 27a 3
9.
( x + 1) 3 + 8
10.
8 y 3 − 27 z 9
Factor the following completely. Remember to:
• look for any GCF’s first
• if two terms, look for differences of squares, or sums or differences of cubes
• if three terms, look for quadratic forms that factor into (
• if four or more even terms, try grouping
) (
)
Answers to part I:
1)
( x + 2 )( x 2 – 2x + 4 )
2)
( 2a + 1)( 4a 2 – 2a + 1)
3)
( x − y )( x 2 + xy + y 2 )
4)
( 4xy – 1)(16x 2 y 2 + 4xy + 1)
5)
(a
+ b ) ( a 4 – ab + b 2 )
6)
( abc − 5 )( a 2b 2 c 2 + 5abc + 25 )
7)
(x
− y 4 ) ( x 20 + x10 y 4 + y 8 )
8)
(b − 3a )(b 2 + 3ab + 9a 2 )
9)
((x + 1) + 2 )((x + 1)2 – 2(x + 1) + 4 )
= ( x + 3) ( x 2 + 2x + 1 – 2x – 2 + 4 )
= ( x + 3) ( x 2 + 3)
10)
( 2y − 3z )( 4y
2
10
Answers to part II:
3
2
+ 6yz 3 + 9z 6 )