Factor Completely:
6x² - 7xy - 5y²
Since there are no common factors to all 3 terms, we proceed:
1. Multiply the 6 by the 5. (Ignore signs for now). Get 30
2. We look at the sign of the last term to see whether to
put SUM or to put DIFFERENCE in the blank in the following step.
3. Think of two positive integers which have product = 30 and
= 7 (ignore the sign for now)
It is a " - ", so we put DIFFERENCE (not SUM) in the blank in
the next step:
So we put DIFFERENCE in the blank. So then we
Think of two positive integers which have product = 30 and
DIFFERENCE = 7 (ignore sign for now)
Certainly if you learned the multiplication facts well in
elementary school, 10 and 3 will quickly come to mind,
since 10×3 = 30 and 10-3 = 7.
4. Look at the middle term of 6x² - 7xy - 5y². It is -7xy.
(Don't ignore sign this time!). Now attach signs to 10 and 3
so that they will combine to give -7. The larger, 10, gets
a - sign and the smaller a positive sign. So we have -10 + 3
so we use that to rewrite the middle term -7xy as
-10xy + 3xy:
So far we have this:
6x² - 7xy - 5y²
6x² - 10xy + 3xy - 5y²
Factor 2x out of the first two terms
Factor y out of the last two terms
2x(3x - 5y) + y(3x - 5y)
Now factor out the GCF which is (3x - 5y)
(3x - 5y)(2x + y)
Edwin
