Question 620914: Using complete sentences, explain how to factor each one. Be sure that the final factorization (or "answer") is a part of your explanation.
10x2 − 7x − 3
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! This is how I do it.
To factor the quadratic trinomial  ,
I first multiply together the absolute values of the leading coefficient (10) and the independent term (-3) to get  .
I look for, and list all pairs of factors that multiply to yield that product, and find 4 such pairs:
 .
One of those pairs will be the absolute values of the coefficients of first degree terms obtained when multiplying the final factorization.
Because the independent term (-3) is negative, I know that those coefficients of first degree terms have opposite signs.
I also know that they add up to the coefficient of the first degree term in the original polynomial (-7).
From the four pairs of factors found above, the pair of factors, with signs, that add up to -7 is
 .
The expanded product of the factorization will contain  and  in addition to the leading and independent terms  and  .
I then organize the expanded product of the factorization in a 2 by 2 square, with the newly found terms at opposite corners:
Next, I look for common factors for each row and column and write them on the same row/column, outside the square.
I find  as a common factor for and , so I write to the left of .
I find  as a common factor for  and , so I write to the left of .
I write  above and , because it is their common factor.
I write  above and , because it is their common factor.
Now I make a binomial of the terms written above the square  and another binomial with the terms written to the left of the square  .
I multiply those binomials to verify that the terms inside the square are generated.
I also verify that collecting terms in that product produces the original trinomial.
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