anonymous
  • anonymous
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anonymous
  • anonymous
what is the sum of the 2 equation x^2-2x-15=0
anonymous
  • anonymous
phi
  • phi
can you rephrase the question?

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anonymous
  • anonymous
thats what it says what is the sum of the 2 solutions to the equation x^2-2x-15=0
phi
  • phi
ok, that makes more sense. (Your first post left out "solutions")
anonymous
  • anonymous
ohhhh ok do u understand it cuz i dont
phi
  • phi
to find the solutions you can factor the expression this is a bit involved. the first step is notice the last number: -15 the minus sign means the solutions will have opposite signs (one will be + and the other -) (if it were +15, the solutions would have the same sign, either both + or both -)
phi
  • phi
next, look at the number in front of the "x" term: -2 because it is negative 2, that means the bigger solution is negative (and from the first step you know the other (smaller) solution is +)
phi
  • phi
now we list all pairs of numbers that multiply to give you 15 (it helps to know rules of divisibility see https://en.wikipedia.org/wiki/Divisibility_rule#Divisibility_rules_for_numbers_1.E2.80.9320) the pairs are 1,15 3,5 those are the only pairs
anonymous
  • anonymous
soo thats means that 15 would be it cuz i dont have a 1, 5 or 3 in my choices
phi
  • phi
make the larger of each pair negative (from the second step) and the smaller of each pair +, and add them +1 - 15 = -15 +3-5 = -2 if any add up to the number in front of the x (ie. add up to -2) we found the pair we write (x+3)(x-5)=0 if you multiply that out using FOIL (if you know how) you get x^2 -2x -15=0 which shows we have the correct factors
anonymous
  • anonymous
whats FOIL i remember it but what does it stand for again
phi
  • phi
finally, we look at (x+3)(x-5)=0 what x number makes that zero? either x+3 =0 (so x= -3) or x-5=0 (so x=5) those are the solutions add them: 5+-3 = 2
anonymous
  • anonymous
ok but whats FOIL again
phi
  • phi
see https://www.khanacademy.org/math/algebra-basics/quadratics-polynomials-topic/multiplying-binomials-core-algebra/v/multiplying-binomials for how to do FOIL
anonymous
  • anonymous
ok and this whats the sum of the polynomials 4x^2y+2x^2y^3 and -2xy +x^2y^3
anonymous
  • anonymous
phi
  • phi
you add them by putting + sign in between them, like this \[ 4x^2y+2x^2y^3 + -2xy +x^2y^3 \] now look for "common terms" (same variables to the same power) do you see any common terms?
anonymous
  • anonymous
yes
phi
  • phi
which terms are "common terms" ?
anonymous
  • anonymous
4x^2 x^2 y^3?
phi
  • phi
you want terms that has the same number of x's and y's
anonymous
  • anonymous
umm ok
phi
  • phi
example: x^2 y and 2 x^2 y or 3x^3 y^3 and 4 x^3 y^3 (you have x^3 and y^3 in both terms.. only the number out front is different)
phi
  • phi
the common terms in your problem are \[ 2x^2y^3 +x^2y^3\] you have 2 of them plus one more. you can write that as \[ 3 x^2y^3\] so the sum is \[ 4x^2y -2xy +3x^2y^3\]

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