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Chapter 5
Pretest
Factor each of the following completely.
1. 20
5xy2( )
5 5
x6 – 34
1. GCF = 5x7y2 – 15x y2 x y2
xy2 xy2
3. Find 2 integers whose product is 10
and sum is 7
1, 10
2, 5
(x )(x )+ 2 + 5
1. GCF = 2. x2 + 7x + 10
Factor each of the following completely.
1
2. Factor first term.
Factor each of the following completely.
3( )
2
3(2x2 + x + 4x + 2 )
1. GCF =
2. Grouping Number.
3
4. Split into 2 terms.
(2)(2) =
3. Find 2 integers whose product is 4 and sum is 5.
1, 4
x2 + 5x + 2
4
6x2 + 15x + 63.
Factor each of the following completely.
(2x + 1)( )
( ) + 2( )
3( )
3
5. Factor by grouping.
3
x 2
x + 2
x 2x + 1 2x + 1(2x + 1) (2x + 1)
2x2 + x + 4x + 2
GCF =
GCF =
GCF =
( )
x
2
(2x + 1)
3( )
2x2 + 5x + 2
6x2 + 15x + 63.
2(6a)(5b) = 60ab
36a2 =
(6a + 5b)2
25b2 =
2. Are the 1st and 3rd terms are perfect squares
√
3. Is 2nd term double the product of the values whose squares
are the 1st and 3rd terms
√
4. 36a2 + 60ab + 25b2
Factor each of the following completely.
1. GCF = 1
(6a)2
(5b)2
x( )
9
1. GCF =
2. Grouping Number.
x
There is none.
(9)(7) =
3. Find 2 integers whose product is 63 and sum is 5.
1, 63
3, 21
7, 9
x2 + 5x + 763
Factor each of the following completely.
9x3 + 5x2 + 7x5.
2ax
(2x – 5)( )
a 3b
a + 3b
-30abx a( )2x – 5 + 3b( )2x – 5(2x – 5) (2x – 5)
– 5a + 6bx – 15b
2. Is the product of 1st and 4th terms = to 2nd and 3rd terms?
6.
Factor each of the following completely.
1. GCF = 1
3. The GCF = a
4. The GCF = 3b
5. The GCF = (2x – 5)
3. Find 2 integers whose product is 15
and sum is 8
1, 15
3, 5
3x + 3 + 5
1. GCF =
3x( )x2 + 8x + 15
7. 3x3 + 24x2 + 45x
Factor each of the following completely.
3x
(x )(x )
2. Factor first term.
3c( )6
3c(6x2 – 8xy + 15xy – 20y2)
1. GCF =
2. Grouping Number.
3c
4. Split into 2 terms.
(6)(-20) =
3. Find 2 integers whose product is -120 and sum is 7.
-1, 120
-2, 60
-3, 40
-4, 30
x2 + 7xy – 20-120
Factor each of the following completely.
18cx2 + 21cxy – 60cy2
y2
-5, 24
-6, 20
-8, 15
8.
( )– 4y
(3x – 4y)( )
+ 5y( )
3c( )
3c
5. Factor by grouping.
3c
2x 5y
2x + 5y
2x 3x 3x – 4y(3x – 4y) (3x – 4y)
6x2 – 8xy + 15xy – 20y2
GCF =
GCF =
GCF =
( )
2x
5y
(3x – 4y)
3c( )6x2 + 7xy – 20y2
Factor each of the following completely.
18cx2 + 21cxy – 60cy28.
9.
Factor each of the following completely.
100x2
(10x + 7y)(10x – 7y)
1. GCF =
( )2
– 49y2
( )2–
1
2. Write as squares10x 7y
3. (sum)(difference)
10.
Factor each of the following completely.
9 4x2
(2x + 1)(2x – 1)
1. GCF =
( )2
– 1
( )2–
9
2. Write as squares
2x 13. (sum)(difference)
36x2 – 9
9
( )
4x2
2(2x)(-3y) = -12xy
1. GCF =
4x2 =
Not a perfect square trinomial
9y2 =
2. Are the 1st and 3rd terms perfect squares
3. Is 2nd term double the product of the values whose squares are the 1st and 3rd terms
√(2x)2
(-3y)2
-12xy ≠ -20xy
1– 20xy + 9y2
Use trial and error or
the grouping method
Factor each of the following completely.
11.
4
4x2 – 2xy – 18xy + 9y2
1. GCF =
2. Grouping Number.
1
4. Split into 2 terms.
(4)(9) =
3. Find 2 integers whose product is 36 and sum is -20.
-1, -36
-2, -18
x2 – 20xy + 9
36
Factor each of the following completely.
11. y2
4x2
(2x – y)( )
2x -9y
2x – 9y
2x 2x – y – 9y 2x – y(2x – y) (2x – y)
5. Factor by grouping.
GCF =
GCF =
GCF =– 2xy – 18xy + 9y2
( ) ( )
Factor each of the following completely.
11. 4x2 – 20xy + 9y2
2x
-9y
(2x – y)
12. 9x2 + 49
PrimeThis not a difference of two
squares.a2 – b2 = (a + b)(a – b)
1. GCF =
Factor each of the following completely.
1
2 1. GCF =
2. Grouping Number.
1
There is none.
(2)(4) =
3. Find 2 integers whose product is 8 and sum is 7.
1, 8
2, 4
x2 + 7x + 4
8
Factor each of the following completely.
13.
Prime
7( )
2
1. GCF =
2. Grouping Number.
7
There is none.
(2)(7) =
3. Find 2 integers whose product is 14 and sum is -8.
-1, -14
-2, -7
x2 – 8x + 714
Factor each of the following completely.
14x2 – 56x + 4914.
Factor each of the following completely.
15. 64x2
(8x + 1)(8x – 1)
1. GCF =
( )2
– 1
( )2–
1
2. Write as squares8x 1
3. (sum)(difference)
4( )
Factor each of the following completely.
16. 4x4 1. GCF =
( )2
– 64
( )2–
4
2. Write as squares
x2 43. (sum)(difference)
x4 16–
(x2 + 4)(x2 – 4)4
(x2 + 4)(x + 2)4 (x – 2)
Factor each of the following completely.
6x2
(2x – 3y)( )
3x 5y
3x + 5y
-90x2y2 3x( )2x – 3y + 5y( )2x – 3y
(2x – 3y) (2x – 3y)
– 9xy + 10xy – 15y2
2. Is the product of 1st and 4th terms = to 2nd and 3rd terms?
17. 1. GCF = 1
3. The GCF = 3x
4. The GCF = 5y
5. The GCF = (2x – 3y)
2( )
2( )3x2
(x + 2)( )
3x -5y
3x – 5y
1. GCF =
-30xy
3x( )x + 2 – 5y( )x + 2(x + 2) (x + 2)
+ 6x – 5xy – 10y
2. Is the product of 1st and 4th terms = to 2nd and 3rd terms?
2
3. The GCF = 3x
4. The GCF = -5y
5. The GCF = (x + 2)
Factor each of the following completely.
18. 6x2 + 12x – 10xy– 20y
2
2( )2
2(2x2 – 5x + 6x – 15)
1. GCF =
2. Grouping Number.
2
4. Split into 2 terms.
(2)(-15) =
3. Find 2 integers whose product is -30 and sum is 1.
-1, 30
-2, 13
-3, 10
-5, 6
x2 + x – 15-30
Factor each of the following completely.
4x2 + 2x – 3019.
1
( )– 5
(2x – 5)( )
+ 3( )
2( )
2
5. Factor by grouping.
2
x 3
x + 3
x 2x 2x – 5(2x – 5) (2x – 5)
2x2 – 5x + 6x – 15
GCF =
GCF =
GCF =
( )
x
3
(2x – 5)
Factor each of the following completely.
2( )2x2 + x – 15 4x2 + 2x – 3019.
x2( )3
x2(3x2 + 4x – 15x – 20)
1. GCF =
2. Grouping Number.
x2
4. Split into 2 terms.
(3)(-20) =
3. Find 2 integers whose product is -60 and sum is -11.
1, -60
2, -30
3, -20
4, -15
x2 – 11x – 20-60
Factor each of the following completely.
3x4 – 11x3 – 20x220.
( )+ 4
(3x + 4)( )
– 5( )
x2( )
x2
5. Factor by grouping.
x2
x -5
x – 5
x 3x 3x + 4(3x + 4) (3x + 4)
3x2 + 4x – 15x – 20
GCF =
GCF =
GCF =
( )
x
-5
(3x + 4)
Factor each of the following completely.
x2( )3x2 – 11x – 20 3x4 – 11x3 – 20x220.
Chapter 5
Pretest