We are now looking for two binomial factors that have the following characteristics:
1. The product of the constant terms is negative 2.
2. The sum of the constant terms is negative 1.
Since the product is negative, the two constant terms must be of opposite sign. The only two integers that have a product of 2 are 2 and 1, so we know that we are looking for either 2 times -1 or -2 times 1.
Since 2 plus -1 is 1, we can discard this choice because we are looking for a sum of -1. -2 plus 1 is -1, so the two integers must be -2 and 1.
That makes the two factors and
Putting it all back together we get:
Now you have 3 factors whose product is zero. That means one of the factors must be zero. We can eliminate 2 because 2 is not and never will be zero. That leaves and , either of which could be zero given an appropriate value for .
If then
If then
Check:
Checks.
Checks.
John
My calculator said it, I believe it, that settles it
