Question 310731: When factoring a trinomial, the last digit, and middle coefficient are important. Explain why.
Found 2 solutions by JBarnum, solver91311:
Answer by JBarnum(2146)   (Show Source):
You can put this solution on YOUR website! to find the factors you will need to find 2 numbers that multiply to get the last digit and add to get the middle coefficient. that is why they are important. they help solve your problem faster.
Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website!
If by "last digit" you mean the constant coefficient, then yes, it is every bit as important as the first degree or linear term coefficient, which I presume you are referring to when you say "middle coefficient." However, neither is any more or less important than the lead coefficient, which is to say the coefficient on the high order term.
Also, the term 'last digit' doesn't really describe what you mean. Consider:  . Here, the 'last digit' could be construed to mean "1" (and quite properly, considering the meaning of the word 'digit'). And, of course, knowing just the last digit in this case is decidedly unhelpful when attempting to factor the expression given.
"Middle coefficient" is rather poor terminology as well. Who says that the first degree term will always be presented "in the middle"?
Proof:
The general solution of a quadratic equation of the form  is:
Notice that all three coefficients,  ,  , and  are required by the formula. Hence, whether the quadratic trinomial is factorable over the rational numbers or not, you still must consider all three coefficients.
Even changing your question so that it reads "When factoring a quadratic trinomial with a lead coefficient of 1,..." doesn't change the fact that you are considering the lead coefficient simply by virtue of the fact that you have restricted it to a value of 1."
No disrespect to your teacher meant, but this is a very poorly worded question.
John
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