Write this
(x )(x )
Think of two POSITIVE whole numbers which multiply to give this
number, 24,........
........that subtract (because of this sign)....,
.......to give this POSITIVE number, 2,.......
So the only two POSITIVE integers that multiply
to give 24 and subtract to give 2, are 6 and 4,
because 6 times 4 is 24 and 6 minus 4 is 2.
So we put 6 and 4 in the parentheses like this:
(x 6)(x 4)
All we need do is put the correct signs in the
middle of each parentheses.
The larger of these two numbers (which is 6 in this case)....
will always get this sign (which is -):
So we put a "-" sign before the 6 in the
first parentheses:
(x-6)(x 4)
Now we need to decide what sign goes in the
middle of the second parentheses:
We look back at this sign:
Since it is a "-" the second parentheses gets
the OPPOSITE sign from the sign in the other
parentheses (so it gets a + ):
(x-6)(x+4)
That's the answer.
---------------------------------
Let's do another problem like that:
x²-9x+14
Write this
(x )(x )
Think of two POSITIVE whole numbers which multiply to give this
number, 14,........
........that add (because of this + sign)....,
.......to give this POSITIVE number, 9,.......
So the only two POSITIVE integers that multiply
to give 14 and add to give 9, are 7 and 2,
because 7 times 2 is 14 and 7 plus 2 is 9.
So we put 7 and 2 in the parentheses like this:
(x 7)(x 2)
All we need do is put the correct signs in the
middle of each parentheses.
The larger of these two numbers (which is 7 in this case)....
will always get this sign (which is -):
So we put a "-" sign before the 7 in the
first parentheses:
(x-7)(x 2)
Now we need to decide what sign goes in the
middle of the second parentheses:
We look back at this sign:
Since it is a "+" the second parentheses gets
the SAME sign as the sign in the other
parentheses (so it also gets a - ):
(x-7)(x-2)
That's the answer.
Edwin
