Problema Solution
Andrew factored the expression 14x^3-21x^2-7x as 7x(14x^2-21x-7). But when Melissa applied the distributive law and multiplied out 7x(14x^2-21x-7), she got 98x^3-147x^2-49x ; thus, Andrew’s solution does not appear to check. Why is that? Please help Andrew to understand this better. Explain your reasoning and correctly factor the original expression, if possible. If the expression is prime, so state.
Answer provided by our tutors
Andrew correctly determined the GCF of 14x^3, -21x^2 and -7x as 7x, but when he took that out as a common factor, he did not divide each term by the GCF 7x.
So, the correct factorization should have been
= 7x (14x^3 / 7x - 21x^2 / 7x - 7x/7x)
= 7x (2x^2 - 3x - 1)
The expression is not prime because there are clearly at least 2 factors.