# Method of Decomposition Lesson 30

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"Method of Decomposition Lesson 30"

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```					     Method of Decomposition
• Sometimes in math it helps to work
backwards to solve a problem.

• With factoring trinomials this is called:
method of Decomposition.
Remember FOIL
• Method of Decomposition relies on your
knowledge of multiplying Binomials.
• If you have a good knowledge of how to
use the concept of FOIL, then the method
of composition should come easy to you.
• F – first term
• O – outside terms
• I – inside terms
• L – last terms
Think about This
x2 – 3x - 40       When there is no number in front of
the x2 we found factors using the
following method:
1) Two numbers that multiply to
give you the last term
2) The same two numbers to give
you the sum of the middle terms
Therefore:
Product of - 40
(x – 8)(x + 5)
Sum of -3
Method of Decomposition
Use this to decompose
When there is a number besides                  the trinomial
one in the front we do the follow:

8x2 + 10x + 3       You multiply the first
constant by the last        8x2 + 4x + 6x + 3
constant to get the       = (8x2 + 4x) + (6x + 3)
product.
Product is + 24                              = 4x(x + 1) + 3(x + 1)
=(x + 1)(4x + 3)
8x2   + 10x + 3     +6 and +4 give the
product of + 24

6x + 4x

Which gives: 8x2 + 4x + 6x + 3
Factor: 6y2 + 19y + 15
Solution:                            Think: What two integers
have a product of +90 and a
sum of +19.
6y2 + 19y + 15
The numbers are +10 and +9
= 6y2 + 9y + 10y + 15
= (6y2 + 9y) + (10y + 15)                    Group to factor

= 3y(2y + 3) +5(2y + 3)                      Factor each bracket

= (2y + 3)(3y + 5)                      Collect common Factors

Expand to check solution is correct
Factor: 2x2 – 7x - 15
Solution:                            Think: What two integers
have a product of -30 and a
sum of -7.
2x2 – 7x - 15
The numbers are -10 and +3
= 2x2 -10x + 3x - 15
= (2x2 -10x) + (3x - 15)                      Group to factor

= 2x(x - 5) + 3(x - 5)                        Factor each bracket

= (2x +3)(x - 5)                        Collect common Factors

Expand to check solution is correct
You Try:
Factor: 9x2 + 15x + 4
Solution:                            Think: What two integers
have a product of +36 and a
sum of +15.
9x2 +15x + 4
The numbers are ? and ?
=
=(         )+(         )                     Group to factor

=                                            Factor each bracket

=                                       Collect common Factors

Expand to check solution is correct
Answer:
Factor: 9x2 + 15x + 4
Solution:                            Think: What two integers
have a product of +36 and a
sum of +15.
9x2 +15x + 4
The numbers are +3 and +12
= 9x2 + 3x + 12x + 4
= (9x2 + 3x) + (12x + 4)                     Group to factor

= 3x(3x + 1) + 4(3x + 1)                     Factor each bracket

= (3x + 1)(3x + 4)                      Collect common Factors

Expand to check solution is correct
You Try:
Factor: 9x2 – 9x - 4
Solution:                            Think: What two integers
have a product of +36 and a
sum of -9.
9x2 – 9x - 4
The numbers are ? and ?
=
=(         )+(         )                     Group to factor

=                                            Factor each bracket

=                                       Collect common Factors

Expand to check solution is correct
Answer:
Factor: 9x2 – 9x - 4
Solution:                            Think: What two integers
have a product of -36 and a
sum of -9.
9x2 – 9x - 4
The numbers are -12 and + 3
= 9x2 -12x + 3x - 4
= (9x2 + 3x) + (-12x - 4)                     Group to factor

= 3x(3x + 1) -4(3x + 1)                       Factor each bracket

= (3x + 1)(3x – 4)                      Collect common Factors

Expand to check solution is correct
Class work
• Make sure you have finished lesson 29(4)
and checked the solutions in the share
folder or blog.

• Do Lesson 30 worksheet

• Remember the solutions are in the share
folder

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