Megan factored the expression as 27x^2-51x-6 as (9x-1)(3x+6) . But when Jacob applied the FOIL principle and multiplied out , (9x-1)(3x+6)he got 27x^2-57x-6 ; 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.

Solution:

The correct factor of the original expression:

27x^2-51x-6 = 3(9x^2-17x-2)= 3(9x+1)(x-2) = (9x+1)(3x-6)

Megan: (9x-1)(3x+6) = 27x^2 +51x-6, not 27x^2-51x-6