Factoring Trinomials of the Type ax^2 + bx +c

There are a variety of methods for factoring trinomials, Complete the square! Use the quadratic formula! Or be a genius and do it in your brain!

AlgebraPerform arithmetic operations on polynomials
LanguageEnglish Language
PolynomialsFactoring Polynomials

Transcript

00:24

The guy in accounting says that the amount of spoilage, or “s”…

00:28

…for producing w number of watermelons per day can be approximated by the formula: [accounting guy discussing formula]

00:34

s equals 6w squared plus 13w plus 2.

00:40

What daily production level will give Jen zero spoilage?

00:45

This looks like a trinomial equation of the type ax squared plus bx plus c; [man points to trinomial equation]

00:50

To find the answer, we’re going to need to factor out the a and the c in the equation.

00:55

We’ll do this by using a table. [Dinosaur jumps on a table]

00:58

Our table has four columns.

01:00

The first involves our “a-term”, 6w squared.

01:05

There are two possible ways to factor 6w squared: 3w and 2w, and 6w and w.

01:13

The second column factors our “c-term”, 2.

01:17

The only possible factors are 2 and 1.

01:20

The third and fourth columns use the previous two columns to decipher possible “b-terms”.

01:26

Combinations of the a-term and c-term factors are combined in the “possible binomial factors” [arrow pointing to binomial factors column]

01:32

column.

01:33

If we take a look at the first row of the first two columns, our possible binomial factors

01:37

come out to:

01:38

(3w + 2) times (2w + 1), and (3w+1) times (2w+2).

01:46

For the second row, we get (6w +2) times (w+1), and (6w+1) times (2+2).

01:55

Then, the sum of the inner and outer products are used to calculate what the b-term for

02:00

that product would be.

02:01

So for (3w +2) times (2w + 1), we take the outer product first, which is 3w times 1, [table of factoring trinomials]

02:10

and add it to the inner products: 2w times 2.

02:14

3w times 1 is 3w, and 2w times 2 is 4w.

02:19

So the sum is 7w.

02:21

Not the right b-term...so we keep trying. [man points to b-term]

02:24

After doing all the calculations, we can see that the factors (6w + 2) and (w + 2) give

02:30

us our correct b-term, 13w, hiding out like a bunny at a fox convention. [fox hiding among bunnies]

02:35

Our work can be checked using FOIL, multiplying out the first terms, outer terms, inner terms,

02:42

and last terms,.

02:44

We add them together…and check to see that they equal our original trinomial. [man looking at the completed formula]

02:50

We passed the checkpoint, which means when spoilage equals zero, one of our factors must

02:55

also equal zero.

02:58

When we set each factor to zero and solve for w…

03:00

…we see there is zero spoilage when our daily watermelon production equals negative

03:05

one sixth and negative 2. [doughnut watermelons appear]

03:07

Uh-oh.

03:08

Since it’s impossible to have negative production…

03:10

…looks like Farmer Jen has no choice but to introduce spoiled watermelons into the [farmer Jen throwing a watermelon into the ocean]

03:16

food supply.

03:17

Good luck, everyone.