We were told to factor this polynomial but I
cannot figure out the Gcf.
4s + 6st - 14st
Those last two terms are like terms, are you sure you
copied it right? Did you leave out an exponent? I'll
assume you didn't and I just won't combine like terms
till the last step:
Prime factor 4s, 6st and 14st
4s = 2·2·s
6st = 2·3·s·t
14st = 2·7·s·t
Line up the factors so that only like factors are
lined up vertically, like this:
4s = 2·2 ·s
6st = 2 ·3 ·s·t
14st = 2 ·7·s·t
There are only two factors that appear in all three
rows, the ones I have colored red and blue:
4s = 2·2 ·s
6st = 2 ·3 ·s·t
14st = 2 ·7·s·t
So the GCF is 2·s
4s + 6st - 14st =
2·2·s + 2·3·s·t - 2·7·s·t
So take out the red and blue factors,
and put all the black ones inside
parentheses along with their signs:
2·s(2 + 3·t - 7·t)
or
2s(2 + 3t - 7t)
Notice that there are two like terms in the parentheses,
+3t and -7t which will give -4t
2s(2 - 4t)
Edwin
