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.
