Answer:
Part A:
To find the total length of the two sides you want to add them together:
(3x^2-2x-1)+(9x+2x^2-2)= you want to combine all like terms
3x^2+2x^2=5x^2, you add your coefficients and keep the exponents the same
-2x+9x=7x, you would combine like terms
-1-2=-3, you would subtract according to Keep, Change, Change
You now have:
5x^2+7x-3= Sides A+B
5x^2+7x-3
Part B:
To find the length of the third side you want to take the perimeter of the triangle and subtract it from our answer in part A
(5x^3+4x^2-x-3)-(5x^2+7x-3)
When subtraction polynomials we want to change the subtraction sign to addition and change the signs of the other number to the opposite sign to prevent making mistakes from subtraction, so you're new equation will look like this:
(5x^3+4x^2-x-3)+(-5x^2-7x+3)
Now we add all like terms again
5x^3, doesn't combine with any others so we leave it the same
4x^2-5x^2=-x^2, subtract them but remember to keep the exponents the same
-x-7x=-8x, again subtract terms but keep variable
-3+3=0, they cancel out so we don't have to worry about putting anything for this one
So now we are left with
5x^3-x^2-8x as our length for the third side
Third side equals 5x^3-x^2-8x
Part C:
For part A we added to get the total of sides B and A
For part B we subtracted the total perimeter from the total lengths of B and A, to figure out what C equals
Hope this helps ;)
