Question

ACT study prep help

Answer 1

what is the sum of the 2 equation x^2-2x-15=0

Answer 2

@phi

Answer 3

can you rephrase the question?

Answer 4

thats what it says
what is the sum of the 2 solutions to the equation x^2-2x-15=0

Answer 5

ok, that makes more sense. (Your first post left out "solutions")

Answer 6

ohhhh ok do u understand it cuz i dont

Answer 7

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 -)

Answer 8

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 +)

Answer 9

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

Answer 10

soo thats means that 15 would be it cuz i dont have a 1, 5 or 3 in my choices

Answer 11

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

Answer 12

whats FOIL i remember it but what does it stand for again

Answer 13

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

Answer 14

ok but whats FOIL again

Answer 15

see
https://www.khanacademy.org/math/algebra-basics/quadratics-polynomials-topic/multiplying-binomials-core-algebra/v/multiplying-binomials

for how to do FOIL

Answer 16

ok and this
whats the sum of the polynomials 4x^2y+2x^2y^3 and -2xy +x^2y^3

Answer 17

@ganeshie8 help

Answer 18

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?

Answer 19

yes

Answer 20

which terms are "common terms" ?

Answer 21

4x^2 x^2 y^3?

Answer 22

you want terms that has the same number of x's and y's

Answer 23

umm ok

Answer 24

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)

Answer 25

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
\[ 4x^2y -2xy +3x^2y^3\]