Cogito
Algebra 1 · Chapter 7 · Lesson 2
Factoring Quadratic Trinomials
Two numbers that multiply and add correctly.
11 problems · about 24 minutes · A-SSE.A.2, A-SSE.B.3
What this lesson teaches
The student factors a quadratic trinomial with leading coefficient one.
- Factoring x² + bx + c needs two numbers multiplying to c and adding to b.
- A positive c means matching signs; a negative c means opposite signs.
- Expanding the factors back is the only check that matters.
Warm Up
Straightforward practice. Get the method working first.
4 problemsMultiply to 18, add to 9. Larger number?
Answer 6
Why 6.
Multiply to 6, add to 5. Larger number?
Answer 3
Why 2 and 3.
Multiply to 15, add to 8. Larger number?
Answer 5
Why 3 and 5.
Multiply to 9, add to 6. Larger number?
Answer 3
Why 3 and 3.
Build It Up
The same ideas with more to keep track of.
3 problemsMultiply to −12, add to 1. Positive number?
Answer 4
Why 4 and −3.
x² + 5x + 6 factors to (x + 2)(x + ?). What is the missing number?
Answer 3
Why 2 × 3 = 6.
A positive constant with a positive middle term. Are both numbers positive? 1 for yes, 0 for no.
Answer 1
Why Shared sign is the sign of b.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsMultiply to 20, add to 9. Larger number?
Answer 5
Why 4 and 5.
Order the steps for factoring x² + bx + c.
Answer 1. List pairs multiplying to c 2. Find the pair adding to b 3. Write the two brackets 4. Expand to check
Why The product narrows the candidates; the sum picks one.
The Pair: Two numbers multiply to 12 and add to 7. What is the larger?
Answer 4
Why 4.
A Negative Constant: Two numbers multiply to −10 and add to 3. What is the positive one?
Answer 5
Why 5.