will post an example of # 3 and instructions for the ac method at the
problems 1 and 2 factor the polynomials using whatever strategy
seems appropriate. State what methods you will use and then
demonstrate the methods on your problems, explaining the process as
you go. Discuss any particular challenges those particular
polynomials posed for the factoring
problem 3 make sure you use the “ac method”, Show the steps of
this method in your work in a similar manner of the example.
the following five math vocabulary words into your discussion. Use
emphasize the words in your writing (Do
not write definitions for the words; use them appropriately in
sentences describing your math work.
b^3 + 49b (Factoring completely)
a^2 + 7ab 10b^2 (Factoring with Two Variables)
-14a +15 (Factor each trinomial using the ac method. Instructions for this method are below)
first step in factoring ax^2 + bx + c with a =1 is to find two
numbers with a product of c and a sum of b. If a cancels out 1, then
the first step is to find two numbers with a product of ac and a sum
of b. This method is called the ac method. The strategy for factoring
by the ac method follows. Note that this strategy works whether or
not the leading coefficient is 1.
to factor the trinomial ax^2 + bx + c:
- Find two numbers that have a product equal to ac and a sum equal to
- Replace bx by the sum of two terms whose coefficients are the two
numbers found in (1).
- Factor the resulting four-term polynomial by grouping.
is an example of #3
– 13b + 6 a = 5 and c = 6, so ac = 5(6) = 30.
pairs of 30 are 1 and 30, 2 and 15, 3 and 10, 5 and 6
-3(-10)=30 while -3+(-10)= -13 so replace -13b by -3b and -10b
– 3b – 10b + 6 Now factor by grouping.
– 3) – 2(5b – 3) The common binomial factor is (5b – 3).
– 3)( b – 2) Check by multiplying it back together