Megan factored the expression 12x^2+13x-14 as (3x+2)(4x-7). But when Jacob applied the foil principle and multiplied out(3x+2)(4x-7), he got 12x^2-13x-14; 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

12x^2+13x-14=
12x^2-8x+21x-14=(12x^2-8x)+(21x-14)=
4x(3x-2)+7(3x-2)=(3x-2)(4x+7)