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How do I explain the correct process used to simplify subtracting polynomials and put it in words

I am having issues with how to word out this whole thing, math is one of my most weakest link as a student especially when it comes to explaining a problem out. I need help simplifying (3x2 -4x +7) – (-5x2 +12x -9) and give your final answer in simplest form. How do I show that my solution is correct by evaluating it for m = -3 in the original expression and in your expression. And what would one situation would be a good example of a real life use of polynomials.

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Thank you so much for your help and very well put explanation of polynomials, it was really understanding and clear.

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1 Answer

Hi Charley;
(3x2 -4x +7) – (-5x2 +12x -9)
Let's first understand that subtracting a negative number, is the same as add a positive number.
Let's also understand that subtracting a positive number is subtraction.
So let's remove the parentheses...
3x2-4x+7+5x2-12x+9
Let's combine like terms...
3x2+5x2=8x2
-4x-12x=-16x
7+9=16
8x2-16x+16
8(x2-2x+2)
 
I do not know how to evaluate it for m=-3.  It is my understanding that the symbol m represents slope of a linear equation.
 
A good example of use of real life polynomials is personal investment.  Is your money going to grow exponentially, or linearly?  Is the change of value in your investment positive or negative?
 
If you invest x dollars into a new house, is such capital investment expected to increase or decrease in value?  Would such rate of change be exponential or linear?
If you invest x dollars into a bank account at a fixed interest rate, it is expected to increase in value.  However, what is the accrual?  Is it exponential or linear?
If you invest x dollars into an education, would your future job, commensurate with such education, amortize such expense?  If so, how much time would it take?  All variables considered, is this exponential or linear financial growth?
EXAMPLE...
Chuck had $10,000 in the bank.  He inherited it from his grandfather with the request that he invest it effectively.
 
He used $1,000 to make the down-payment on a small plot of land upon which he expected he would one day build a house.  A bank loan covered the remaining balance of the purchase.  He then purchased a small, used trailer for $1,500.  He moved in the next day.
 
Chuck then went to the bank, and invested $500 in a savings account which paid 2% interest.  The $7,000 which remained was used for tuition payment at a computer learning center.  It was a one-year program.  He expected to graduate and find immediate employment in the job market at a starting salary of $25,000/year.