Question

3.4 MIXED FACTORING

1. Utilize all of the strategies for factoring in order to factor the following polynomials.
Reminder: Combine like-terms prior to factoring.

-7n + 5n^2 + 6 - 3n^2 - 11n + 30

Answer 1

2 (n - 3) (n - 6)

Explanation:

`-7n+5n^2+6-3n^2-11n+30`

Group like terms and combine...

`2n^2-18n+36`

Observe that all terms contain a factor of 2. Factor out a 2...

`2(n^2-9n+18)`

The leading coefficient is 1. The shortcut applies. Find the factors of "c" (18)

• 18 = 1 * 18
• 18 = 2 * 9
• 18 = 3 * 6

Of these factor pairs, -3 & -6 will multiply to make 18, and add to make -9 (the "b").

Finish factoring the trinomial into two binomials:

`2(n-3)(n-6)`

To verify that this is a valid factoring, distribute, and recombine terms:

`2(n-3)(n-6)`

`2(n^2-3n-6n+18)`

`2(n^2-9n+18)`