Answer: {-1/7, 3}
Step-by-step explanation: Since this polynomial equation is already set equal to 0, we can go ahead and factor right away.
Note: There are different methods teachers chose to factor with and I recommend using the guess and check method, the most straightforward one I know of and very easy for students to understand.
When factoring, we know we will end up with two sets of binomials.
So we can write them as ( )( ).
We know 7x² factors as 7x · x so we can put a 7x
in our first binomial and an x² in our second binomial.
So we have (7x )(x ).
However, what goes in our second?
Well the factors of -3 will go in our second
but -3 factors in different ways.
-3 factors as -3 · +1, or +1 · -3 and since our binomials
are not identical, we have to also consider reversing the order
That is +3 · -1 or -3 · +1.
If you foil the outer and inner terms for each pair, you should
find the pair that works will be +1 and -3.
So we can write this as (7x + 1)(x - 3) = 0.
Now we use the zero product property:
So either 7x + 1 = 0 or x - 3 = 0.
From here, you should be able to easily solve to get {-1/7, 3}.