Week 19: Factoring trinomials, and the first probability

Field Book

68 to 71

Due

Test 16 due

Method

Paper first, every step

Factoring a trinomial is running multiplication backwards. You have the answer and you are asked for the two things that were multiplied to get it. Every quadratic you meet for the rest of the year opens with this move, so it is worth being fast at. Probability arrives alongside it and asks a different question entirely: not what is true, but how often.

What you have to be able to do

Factor a trinomial into two binomials
Pull out a common factor before factoring
Compute a simple probability, including in a designated order

The procedures

Factoring a trinomial

Look at the last number and the middle number. You need two values that multiply to the last one and add to the middle one.
List the factor pairs of the last number and check which pair adds correctly. Watch the signs.
Those two values are the constants in your two binomials.

Common factor first

Before anything else, check whether every term shares a factor.
Pull it out front. What is left inside is smaller and easier to factor.
Do not lose the factor you pulled out. It stays in the final answer.

Probability

Probability is favorable outcomes over total outcomes.
For a designated order, multiply the probability of each pick in turn.
If you do not replace what you drew, the total shrinks for the next pick.

Worked

WORKED

Factor x² + 7x + 12.
Two numbers multiplying to 12 and adding to 7. The pairs of 12 are 1 and 12, 2 and 6, 3 and 4.
3 and 4 multiply to 12 and add to 7.
ANSWER: (x + 3)(x + 4)

WORKED

Factor 2x² + 10x + 12.
Every term is divisible by 2. Pull it out: 2(x² + 5x + 6).
Now factor the inside: 2 and 3 multiply to 6 and add to 5.
ANSWER: 2(x + 2)(x + 3)

Terms

Term	Meaning
trinomial	a polynomial with three terms
binomial	a polynomial with two terms
probability	favorable outcomes divided by total outcomes

Check yourself

1. Factor x² + 8x + 15

2. Factor 3x² + 12x + 9

3. A bag holds 3 red and 5 blue marbles. Probability of drawing red?

reveal answers

(x + 3)(x + 5) · 3(x + 1)(x + 3) · 38

This page is the summary, not the lesson. The full working, every step of every example, is on the board in class. Come here to remember what the week was about. Go there to learn how it is done.