hFactor 3z^2+14z +8
We try to factor it.
Multiply the 3 by the 8, get 24. Write down all the ways
you can multiply two positive integers together to get 24.
They are
1x24
2x12
3x8
4x6
Now since the last sign before the 8 is +, out to the
right of those we ADD those pairs of positive integers:
1x24 1+24=25
2x12 2+12=14
3x8 3+8=11
4x6 6+4=10
Ignoring signs we see that 14 is the coefficient of the
middle term, and that corresponds to factors 2 and 12,
So we must put signs, either + or -, in front of 2z and 12z
so they will combine to give the middle term, +14z. We
can do that by assigning a positive sign to 2z and a
positive sign to 12z. So the middle term +14z can be
written as +2z+12z
So
becomes
Factor only the first two terms:
Factor the last two terms:
Now notice there is a common binomial factor of
, so we can factor it out:
That's it!
Edwin
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