this week in math 10 i learned how to make a trinomial that has the “pattern” ( , x, #) look “nicer” if it was written out in a jumbled up order. ex 5x-+40 is written as x, , # rather than , x, #. so we can write it as – +5x+40 now, the is negative so when we find the greatest common factor, we can take -5 instead of +5 to make it positive, which would also switch the other terms to their opposites, so – +5x+40 is now -5( -x-40)
this week in math 10 I learned that if we have a binomial that says for example, this is considered a perfect square because = (x)(x) , 81= (9)(9). there is no middle term because when factored it would look like (x-9)(x+9), then if you were to expand this back out, the -9 and the +9 would cancel out and become 0, leaving the answer to be a binomial instead of a trinomial. (x)(x)= + (x)(9)= +9x (-9)(x) = -9x (-9)(9) = -81
+ 9x – 9x -81 . the +9x and the -9x cancel out to be zero
for this to be a “perfect square” we need to make sure that each term is a perfect square and that the sign is subtraction, not addition
this week we started our unit on polynomials, this was mainly review but i learned how to model binomials multiplied by binomials or binomials multiplied by trinomials or trinomials by trinomials etc, by using an area model. i also learned that you can use this type of model to model more than one digit number multiplication. for modeling polynomials, its all done in a box. if i had ( )(x-5) you would draw a square and divide it into 4 even squares, one for each piece of the expression and along the top you would write then along the side you would write x-5 and you would fill in the box as if it were a multiplication chart so it would look like this….
then you add all of the squares together and combine like terms to get a simplified expression
