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She deposited two amounts, let's say "a" and "b"
"a" earning 2% interest
"b" earning 2.5% interest
the 2.5% one, is twice as much as the 2% one
so.. one can say that, whatever "a" is, "b" is twice as much,
or b = 2*a -> b = 2a
now.. .the sum of both earned interest, was $1190
so.. one can say that (2% of a) + (2.5% of b) = 1190
let' us use the decimal notation then
solve for "a" to find what the "a" amount is,
to find "b", well, "b" is "2a", so just do a 2*a to get "b"
"a" earning 2% interest
"b" earning 2.5% interest
the 2.5% one, is twice as much as the 2% one
so.. one can say that, whatever "a" is, "b" is twice as much,
or b = 2*a -> b = 2a
now.. .the sum of both earned interest, was $1190
so.. one can say that (2% of a) + (2.5% of b) = 1190
let' us use the decimal notation then
solve for "a" to find what the "a" amount is,
to find "b", well, "b" is "2a", so just do a 2*a to get "b"
we are given
We will use rational root theorem to find factors
We can see that
Leading coefficient =1
constant term is 6
so, we will find all possible factors of 6
now, we will check each terms
At x=-2:
We can use synthetic division
we get
so, x+2 will be factor
and we can write our expression from synthetic division as
now, we can find factor of remaining terms
we can use quadratic formula
we can compare our equation with quadratic equation
we get
now, we can plug these values
so, we get
so, we can write factor as
so, we get completely factored form as
...............Answer
