factor
2w² - 13w + 18
2x² - 13w + 18
1. Multiply the 2 by the 18, get 36.
2. Notice the sign of the last term is +, so we think "SUM".
(If the sign of the last term had been +, we would think "DIFFERENCE")
3. Think of two positive integers which have product 36 and SUM 13,
the coefficient (in absolute value) of the middle term.
It doesn't take long to see that two such positive integers are
9 and 4. That's because 9 TIMES 4 is 36 and 9 PLUS 4 is 13.
4. Now use 9 and 4 to rewrite the 13 as (9 + 4)
2w² - (9 + 4)w + 18
5. Remove the parentheses by distributing
2w² - 9w - 4w + 18
6. Factor by grouping. That is:
a. Factor the first two terms by taking
out w.
b. Factor the last two terms by taking out -2
w(2w - 9) - 2(2w - 9)
c. Now notice that (2w - 9) is contained in both expressions:
w(2w - 9) - 2(2w - 9)
d. So factor out the whole (2w - 9) leaving w when factoring
it out of the left expression, and leaving -2 when factoring
(2w - 9) out on the right expression.
(2w - 9)(w - 2)
That's it!
Edwin
