Use the GCF to factor the expression 28n + 42.

Question

1. Use the GCF to factor the expression 28n + 42. Explain how you determined the GCF and how you can know that this is the greatest common factor without listing all possible factorizations for the expression.

Answer 1

28n+42 = 14(2n+3)

factor the constants into prime factors

42 = 2x21 = 3x2x7

28 = 14x2 = 2x2x7

common to both is 2x7 or 14

divide by 14 to get 14(2n+3)

or if you want, factor it further to get (2)(7)(2n+3)