Vocabulary
Linear expressions can be multiplied together.
This is often refered to as multiplying out brackets, for example,
(x + 1)(x + 2)= x2 + 3x +
2
The reverse of multiplying out brackets, ie writing
x2 + 3x + 2=(x + 1)(x + 2) is
called factorising. |
We will look at how to factorise
quadratic functions when this can be done "by inspection". This means you
should be able to do it by a combination of mental arithmetic and trial and
improvement.
Example: factorise x² +
4x + 3
| Step 1: |
Write down some "empty"
brackets |
x² + 4x +
3= |
(
)( ) |
| Step 2: |
The first terms in each bracket must both
be x: |
|
(x
)(x ) |
| Step 3: |
The last terms in each bracket must
multiply to give 3. Try* 3 and
1 |
|
(x + 3)(x +
1) |
| Step 4:
|
Check that you get the correct result when
you multiply out the brackets: |
|
|
Sometimes one or both of the
numbers involved may be negative:
Example: factorise x² - 2x - 3
| Step 1: |
Write down some "empty"
brackets |
x² - 2x -
3= |
(
)( ) |
| Step 2: |
The first terms in each bracket must both
be x: |
|
(x
)(x ) |
| Step 3:
|
The last terms in each bracket must
multiply to give -3. Try* 1 and
-3 |
|
(x + 1)(x -
3) |
| Step 4: |
Check that you get the correct result when
you multiply out the brackets: |
|
|
Try*: Your
first attempt may not be correct, if so try again with two other numbers that
multiply to give the required value.
|
