Please help factor completly
21 + 4x - x²
Put a "1" just before the x²
21 + 4x - 1x²
Multiply the 21 by the 1. You get 21. Now we
ask ourselves this question:
What pair of positive integers have product 21
and DIFFERENCE of 4
(I said DIFFERENCE here since the last sign is -. If
it had been +, I would have said SUM)
The answer to the question above is the pair 7 and 3.
That's because their product is 21 and their
difference is 4.
Consider these as representing 7x and 3x.
Now we attach signs to 7x and 3x so that they will
combine to the middle term + 4x. To do that we attach
a "+" to the 7x and a "-" to the 4x, because
+ 4x = + 7x - 3x
So we replace "+ 4x" by "+ 7x - 3x", and so,
21 + 4x - 1x² becomes
21 + 7x - 3x - 1x²
Now we factor 7 out of the first two terms, and -1x
out of the last two terms:
7(3 + x) - 1x(3 + x)
Now we factor (3 + x) out of both terms
(3 + x)(7 - 1x)
We can erase the 1 and the final answer is
(3 + x)(7 - x)
Edwin
