Factorizing Algebraic Expressions Worksheet Page 6
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18Section 4
Factorizing Quadratics
Before we start factorizing quadratics, it would be a good idea to look for a pattern.
2
(x + 2)(x + 4) = x
+ 4x + 2x + 8
2
= x
+ 6x + 8
Notice that the numbers 2 and 4 add to give 6 and multiply to give 8.
2
(x + 5)(x
3) = x
3x + 5x
15
2
= x
+ 2x
15
Notice that the numbers 5 and
3 add to give 2 and multiply to give
15.
Let’s try to factorize expressions similar to those above, where we will start with the expression
2
in its expanded out form. To factorize the expression x
+ 7x + 12, we will try to find numbers
that multiply to give 12 and add to give 7. The numbers that we come up with are 3 and 4,
so we write
2
x
+ 7x + 12 = (x + 3)(x + 4)
This equation should be verified by expanding the right hand side.
2
Example 1 : Factorize x
+ 9x + 14.
We attempt to find two numbers that add to give 9 and multiply to give 14, and
the numbers that do this are 2 and 7. Therefore
2
+ 9x + 14 = (x + 2)(x + 7)
x
Again, this equation shouldn’t be believed until the right hand side is expanded,
2
and is shown to equal x
+ 9x + 14.
2
Example 2 : Factorize x
+ 7x
18.
We attempt to find two numbers that add to give 7 and multiply to give
18
(notice the minus!). The numbers that do this are
2 and 9. Therefore
2
+ 7x
18 = (x
2)(x + 9)
x
This equation shouldn’t be believed until the right hand side is expanded, and is
2
shown to equal x
+ 7x
18.
Page 6
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