Question

I've worked this problem like I was shown but I'm doing something wrong because my answer is not correct, can someone help please and thank you

Megan factored the expression 18x^2 – 57x + 35 as (6x – 7)(3x – 5). But when Jacob applied the FOIL principle and multiplied out (6x – 7)(3x – 5), he got 18x^2 – 51x + 35; thus, Megan’s solution does not appear to check. Why is that? Please help Megan to understand this better. Explain your reasoning and correctly factor the original expression, if possible. If the expression is prime, so state.

Answer 1

I'm not too clear on how Megan has factored the equation so let's assume it was by hand and something like this:
( Ax -5)( Bx -7) Assume it is 5 and 7 (if it doesn't work out we will have to test 35 and 1, the other not so likely choice).
They have to be both negative because if they were both plus you couldn't get -57x.
Now FOIL says -5*Bx +-7*Ax = -57x and we should test out likely values of A and B to see what works
etc etc

Answer 2

Oh ok, I forgot that there are multiple numbers that can be used and went with the first thing that came to mind. Thanks :)