What is factoring by grouping? When factoring a trinomial by grouping, why is it necessary to write the trinomial in four terms?
2 answers
math help needed.
In this method you are basically reversing the steps of multiplying a binomial times a binomial by FOIL
Let me illustrate with an example
expand (2x+3)(5x-4)
= 10x^2 - 8x + 15x - 12
notice that in the original expansion there are four terms
= 10x^2 + 7x - 12
Suppose you were given 10x^2 + 7x - 12 to factor. (of course you would not see the above expansion)
the trick is to separate the 7x into its original two components,
so the middle term will be re-written as the sum of two terms
which means you now have four terms.
I assume you know the actual method of proceeding from here, and you just needed an explanation why there are four terms.
Let me illustrate with an example
expand (2x+3)(5x-4)
= 10x^2 - 8x + 15x - 12
notice that in the original expansion there are four terms
= 10x^2 + 7x - 12
Suppose you were given 10x^2 + 7x - 12 to factor. (of course you would not see the above expansion)
the trick is to separate the 7x into its original two components,
so the middle term will be re-written as the sum of two terms
which means you now have four terms.
I assume you know the actual method of proceeding from here, and you just needed an explanation why there are four terms.
4 answers