This week in Math 10 we started polynomials we were taught many methods on how to solve polynomials such as the tile method, the box/square method and the claw/foil method. A question that was new to me and I had problems with was: A binomial multiplied by a trinomial with a 2 on the outside of the bracket.
There were many ways I could have approached this equation, I could have drew tiles or used the box method, which shows a more visual way of solving the polynomial. I could have used the claw method first or distributed the 2 to the first bracket first. But the first time I tried this question I went straight to the claw method. When doing the claw method/foil method you need to distribute the (5x+2) to the (3x^2+x-4), in order to do this you multiply the 5x by all the terms in the second bracket and then you multiply the 2 by all the terms in the second bracket. This method I used was fine but somehow I got a different answer, the reason I got it wrong was because after using the claw/foil method I assumed I got rid of all the brackets and combined all the like terms when really the 2 still wasn’t distributed yet. Then I asked myself if I changed the order of my steps could this mistake have been prevented.
On my second attempt of trying this question I distributed the 2 to the first bracket first, so basically I multiplied 2 by 5x and then 2. After doing this I was able to get rid of the first bracket. Then I realized There was a need to do the claw/foil method one more time, after doing the foil method one more time then I could finally combine all the like terms.
During class we learned a trick that works for a binomial multiplied by a binomial. I realized that trick did not work for this specific problem since there was a trinomial.
I also used the FOIL method when solving this equation:
F– first
O– outside
I– inside
L-last
this is a simple rule to follow but for this specific equation I had to apply the FOIL method on a larger scale.
Overall this equation taught me there is no specific rule you can follow to solve polynomials there are methods you can use but you have to know how to apply those rules to the specific equation you are trying to solve.