Chapter 8.3--Factoring Polynomials of the form

Factoring polynomials of the form is usually
d one in one of two ways .

**Part 1 Factoring by trial (and error)**

Given the trinomial
find the factors of both a and c . Then check to see which products of these
factors add up to b .

**Question 7:** Factor

Factors of

Now test all the combinations of binomial pairs (until you
get one that works).

In this case the last one we tried worked. We could have
shortened our trials if we noticed that since the middle term of the problem is
negative , we wouldn't have to test the positive factors .

**Question 6 Now you try this one:**

Factors of

Now test all the combinations of binomial pairs (until you
get one that works).

The answer is

**Question 53:** Factor

Take out the common factor first:

The factors are

**Question 38:**

So the factors are

**Part 2 Factoring by grouping **

Algorithm: In the trinomial
multiply ac . Then find all the
factors of ac .Find the pair r,s that add up to b , and rewrite the
trinomial as . Finally factor
this by grouping. |

**Question 78: **Factor

All the factors of
are:

1,40 sum is 41

2,20sumis22

4,10 sum is 14

5,8 sum is 13

I used "sum" because the last coefficient is positive

Use minus because the middle coefficient is negative

Now factor by grouping:

**Question 71 Now you do this one: **Factor

ac = 15

Write down all the factors of ac =15

1,15 their sum is 16 (This is what we want.)

3,5 their sum is 8

factor by grouping.

**Question 107:** Factor

Factor out the common factor first:

Multiply 2 and 5

Factors of 10 are

1,10 their difference is 9

2,5 their difference is 3