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KS3-NA11-4-f2-4/p.1 of 2
Learning Unit：Factorization of Simple Polynomials-Cross Method Exercise
Cross Method Exercise（3）
1.
Using the following diagram, factorize 2 x 2  7 x  3 .
2x
1
3
x
3
1
7x
Sum of products of
5x
-1
-3
-3
-1
-7x
-5x
diagonal pairs=
2x 2  7 x  3  
2.


Using the following diagram, factorize 2 x 2  x  6 .
2x
1
2
3
x
-6
-3
-2
(
Sum of products of
)(
)(
)(
6
-1
-1
6
)(
-2
3
)(
-3
2
)(
-6
1
) (
)
diagonal pairs =
2x 2  x  6  
3.


Using the following diagram, factorize 3x 2  10 x  7 .
3x
1
7
x
7
1
(
Sum of products of
)
(
)
-1
-7
(
-7
-1
)
(
)
diagonal pairs =
3x 2  10 x  7  
4.


Complete the following diagram, the use it to factorize 3 x 2  2 x  8 .
3x
1
2
4
8 ( ) (
x
-8
-4
-2
-1 ( ) (
(
Sum of products of
)(
)(
)(
)(
)(
)
)
(
(
)(
)
)
(
(
) (
)
)
)
diagonal numbers =
3x 2  2 x  8  
5.


Complete the following diagram, the use it to factorize 3x 2  5 x  8 .
3x
( ) ( ) ( ) ( ) ( ) (
x
( ) ( ) ( ) ( ) ( ) (
(
Sum of products of
)(
)(
)(
)(
diagonal pairs =
3x 2  5 x  8  


)(
)
)
)(
(
(
)
)
) (
(
(
)
)
)
KS3-NA11-4-f2-4/p.2 of 2
Learning Unit：Factorization of Simple Polynomials-Cross Method Exercise
Cross Method Exercise（3）（Answers）
1. Using the following diagram, factorize 2 x 2  7 x  3 .
2x
1
3
x
3
1
7x
Sum of products of
5x
-1
-3
-3
-1
-7x
-5x
diagonal pairs =
2 x 2  7 x  3  2 x  1x  3
2. Using the following diagram, factorize 2 x 2  x  6 .
2x
1
2
3
x
-6
-3
-2
( -11x )
Sum of products of
( -4x )
( -x )
6
-1
-1
6
-2
3
-3
2
-6
1
( 4x ) ( 11x )
( 4x )
(x)
( -4x )
diagonal pairs =
2 x 2  x  6  2 x  3x  2
3. Using the following diagram, factorize 3x 2  10 x  7 .
3x
1
7
x
7
1
( 22x )
Sum of products of
( 10x )
-1
-7
-7
-1
( -22x )
( -10x )
diagonal pairs =
3x 2  10 x  7  3x  7x  1
4. Complete the following diagram, the use it to factorize 3 x 2  2 x  8 .
3x
1
2
4
8
( -1 ) ( -2 )
x
-8
-4
-2
-1 ( 8 ) ( 4 )
( -4 )
( 2 )
( -8 )
( 1 )
( 5x ) ( 23x ) ( 10x )
( 2x )
( -5x )
5. Complete the following diagram, the use it to factorize 3x 2  5 x  8 .
3x
( 1 ) ( 2 ) ( 4 ) ( 8 ) ( -1 ) ( -2 )
x
( -8 ) ( -4 ) ( -2 ) ( -1 ) ( 8 ) ( 4 )
( -4 )
( 2 )
( -8 )
( 1 )
(2x )
( -5x )
( -23x )
Sum of products of
(-10x)
( -2x )
diagonal pairs =
3x 2  2 x  8  3x  4x  2
( -23x ) ( -10x )
Sum of products of
( -2x )
diagonal pairs =
3x 2  5 x  8  3x  8x  1
( 5x ) ( 23x ) ( 10x )